Methods and apparatus for obtaining diagnostic information relating to an industrial process

ABSTRACT

In a lithographic process, product units such as semiconductor wafers are subjected to lithographic patterning operations and chemical and physical processing operations. Alignment data or other measurements are made at stages during the performance of the process to obtain object data representing positional deviation or other parameters measured at points spatially distributed across each unit. This object data is used to obtain diagnostic information by performing a multivariate analysis to decompose a set of vectors representing the units in the multidimensional space into one or more component vectors. Diagnostic information about the industrial process is extracted using the component vectors. The performance of the industrial process for subsequent product units can be controlled based on the extracted diagnostic information.

This application is a continuation of pending U.S. patent applicationSer. No. 15/915,674, filed Mar. 8, 2018, which is a continuation ofpending U.S. patent application Ser. No. 15/025,856, filed Mar. 29,2016, which is the U.S. national phase entry of PCT patent applicationno. PCT/EP2014/068932, which was filed on Sep. 5, 2014, which claims thebenefit of priority of U.S. Provisional Patent Application No.61/885,977, filed Oct. 2, 2013, which is incorporated by referenceherein in its entirety.

FIELD

This disclosure relates to methods of obtaining diagnostic informationrelating to an industrial process. An example of an industrial processfor which the method has been developed is a lithographic process, whichincludes one or more steps of transferring a pattern from a patterningdevice onto a substrate using a lithographic apparatus. This disclosurefurther relates to a diagnostic apparatus, to a device manufacturingmethod, to a controller for an industrial process, and to a computerprogram product for causing a data processing apparatus to implement themethods and apparatus described.

RELATED ART

A lithographic process is one in which a lithographic apparatus appliesa desired pattern onto a substrate, usually onto a target portion of thesubstrate, after which various processing chemical and/or physicalprocessing steps work through the pattern to create functional featuresof a complex product. The accurate placement of patterns on thesubstrate is a chief challenge for reducing the size of circuitcomponents and other products that may be produced by lithography. Inparticular, the challenge of measuring accurately the features on asubstrate which have already been laid down is a critical step in beingable to position successive layers of features in superpositionaccurately enough to produce working devices with a high yield.So-called overlay should, in general, be achieved within a few tens ofnanometers in today's sub-micron semiconductor devices, down to a fewnanometers in the most critical layers.

Consequently, modern lithography apparatuses involve extensivemeasurement or ‘mapping’ operations prior to the step of actuallyexposing or otherwise patterning the substrate at a target location.So-called advanced alignment models have been and continue to bedeveloped to model and correct more accurately non-linear distortions ofthe wafer ‘grid’ that are caused by processing steps and/or by thelithographic apparatus itself. Not all distortions are correctable,however, and it remains important to trace and eliminate as many causesof such distortions as possible.

BRIEF SUMMARY

Modern lithographic process and products are so complex that issues dueto processing are difficult to trace back to the root cause. Overlay andalignment residuals typically show patterns over the wafer (of theprocess and/or litho tool). This may be interpreted as a non-correctablequantity with respect to a predefined model, while visual inspection anddetailed analysis of the fingerprint may give an indication of causesand correction strategies. The spatial pattern in the fingerprint is notused to quantify the fingerprint, nor the observation that multiplecauses may show up simultaneously in the apparent fingerprint. Overlaymeasurements are not generally available for each individual wafer, andthe relation to the processing history and context is not generallyknown or used. Furthermore, it is difficult and time-consuming to make alist of all possible sources of spatial variation for the machine andprocess at hand.

Aside from the problem of identifying causes of processing errors,process performance monitoring systems have been implemented which allowmeasurement of performance parameters to be made from processedproducts, which then are used to calculate corrections for use inprocessing subsequent products. A limitation with current performancemonitoring systems is that there is a compromise between the amount oftime and equipment dedicated to performance monitoring, and the speedand accuracy with which corrections can be implemented.

It would also be desirable to have a performance monitoring system thatcan detect problems at an early stage, rather than only detecting themwhen some performance parameter exceeds permissible limits.

The inventors have recognized that root cause finding, monitoring ofwafer integrity and design of an appropriate correction strategy istherefore a subjective and laborious exercise. An embodiment of theinvention aims to provide automated support that addresses one or moreof the problems with known techniques, identified above.

In an aspect, there is provided a diagnostic apparatus for use inrelation to an industrial process, the apparatus comprising a dataprocessing apparatus programmed to perform the steps of:

-   -   receiving object data for a set of product units that have been        subjected nominally to the same industrial process, the object        data for each product unit representing one or more parameters        measured on the product unit at points spatially distributed        across the product unit;    -   defining a multidimensional space in which the object data for        each of the product units can be represented as a vector;    -   performing a multivariate analysis on the object data to obtain        one or more component vectors in the multidimensional space; and    -   extracting diagnostic information about the industrial process        using the component vectors.

In some embodiments, the multivariate analysis is performed on arepresentation of the object data that comprises a set of vectors in themultidimensional space, each of the vectors corresponding to one of theproduct units (or a group of product units). Such a vector may haveelements representing measurements at different ones of the pointsspatially distributed across the product unit. In such animplementation, the object data prior to the multivariate analysis andthe component vectors obtained by the multivariate analysis are bothexpressed as vectors in the same multidimensional space.

Alternative implementations are possible, in which the object data priorto the multivariate analysis is expressed as vectors in a differentmultidimensional space from the one in which the component vectors areexpressed. Conversion between these spaces may be performed (explicitlyor implicitly) either during or after the multivariate analysis. Forexample, in one alternative implementation, the object data is expressedin vectors of which each vector corresponds to one of the points and haselements representing measurements at the point across different ones ofthe product units. In another alternative, multivariate analysis isperformed on the object data without expressing it as vectors in anyparticular multidimensional space.

In an aspect, there is provided a method of obtaining diagnosticinformation relating to an industrial process, the method comprising:

-   -   receiving object data for a set of product units that have been        subjected nominally to the same industrial process, the object        data for each product unit representing one or more parameters        measured on the product unit at points spatially distributed        across the product unit;    -   defining a multidimensional space in which the object data for        each of the product units can be represented as a vector;    -   performing a multivariate analysis on the object data to obtain        one or more component vectors in the multidimensional space; and    -   extracting diagnostic information about the industrial process        using the component vectors.

In an embodiment, the industrial process comprises a sequence of one ormore lithographic processing steps performed on product units in theform of substrates, each lithographic processing step comprising one ormore lithographic patterning operations followed by one or more physicaland/or chemical processing operations. Alignment procedures inlithography generally involve measurements to made automatically acrossthe substrate. These measurements can be captured and represented in theobject data. In this way, the method of an embodiment of the inventionin its most basic form can be implemented without requiring specialmeasurements data capture, or knowledge of the processing context. Themethod is not limited, however, to the use of alignment measurements,nor is it limited in operation to lithographic processes.

The results of the multivariate analysis can be used in various ways toextract diagnostic information. Parts of the extraction can beautomated, other parts can be user-driven, based on visualizationsgenerated by the apparatus. The step of extracting diagnosticinformation may for example include designating certain product units asproduct units of interest based on the positions of their vectors whenprojected onto one or more of the component vectors.

The step of extracting diagnostic information may further comprisecorrelation observed between product units being designated as ofinterest according to the projection of their vectors onto the selectedvector(s) and product units designated as of interest according toperformance data representing one or more performance parametersmeasured for each product unit.

The step of extracting diagnostic information may further comprisereceiving and using context data for each of the product units, thecontext data representing one or more parameters of the industrialprocess as applied to each individual product unit. The step ofextracting diagnostic information may for example comprise identifyingcorrelation between the identification of product units as being ofinterest based on the component vectors and one or more parameters inthe context data.

In other embodiments, the step of extracting diagnostic informationcomprises:

-   -   receiving sparse object data for one or more further product        units that have been subjected nominally to the same industrial        process as the set of product units, the sparse object data for        the further product unit(s) representing the one or more        parameters measured on the product unit(s) at points spatially        distributed across the product unit with a lower density than        the measurements received for the set of product units,    -   analyzing the sparse object data by reference to at least a        subset of the component vectors identified by the multivariate        analysis; and    -   combining the sparse object data with the component vectors in        accordance with the result of the analyzing step, thereby to        reconstruct object data representing the one or more parameters        measured on the further product unit(s) at points spatially        distributed across the product unit with a higher density than        the sparse object data.

One embodiment of the type just mentioned can be used in a performancemonitoring system for the industrial process, where the sparse objectdata is monitoring data relating to a performance parameter of theindustrial process.

The method may further comprise the step of generating one or more setsof correction data for use in controlling the industrial process whenperformed on further product units. The correction data may be appliedfor example as alignment corrections in a future lithographic step tocorrect distortions of the products introduced by a chemical andphysical processing steps. The corrections may be applied selectivelybased on context criteria. The corrections may be applied so as tocorrect some of the identified component vectors and not others.

Where the industrial process comprises a mixture of lithographicpattering operations and physical and/or chemical operations, thediagnostic apparatus may be programmed to generate the correction datafor applying corrections in a lithographic pattering operation.

The apparatus may further comprise a controller arranged to control alithographic apparatus by applying corrections based on the extracteddiagnostic information.

In aspect, there is provided a method of controlling an industrialprocess in which product units are subjected to one or more processingoperations, the method comprising:

-   -   measuring a plurality of product units that have been subjected        to some or all of the processing operations to obtain object        data representing for each product unit one or more parameters        measured on the product unit at points spatially distributed        across the product unit;    -   using the object data to obtain diagnostic information by a        diagnostic apparatus or method according to the invention as set        forth above; and    -   controlling the performance of the industrial process for        subsequent product units based on the extracted diagnostic        information.

In an aspect, there is provided a computer program product comprisingmachine readable instructions for causing a general purpose dataprocessing apparatus to perform the steps of a method for obtainingdiagnostic information as set forth above. The computer program productmay further comprise machine readable instructions for causing the dataprocessing apparatus to generate correction data and optionally contextcriteria.

In an aspect, there is provided a computer program product comprisingmachine readable instructions for causing a general purpose dataprocessing apparatus to perform the steps of a method of controlling anindustrial process as set forth above.

Further features and advantages of the invention, as well as thestructure and operation of various embodiments of the present invention,are described in detail below with reference to the accompanyingdrawings. It is noted that the invention is not limited to the specificembodiments described herein. Such embodiments are presented herein forillustrative purposes only. Additional embodiments will be apparent topersons skilled in the relevant art(s) based on the teachings containedherein.

BRIEF DESCRIPTION OF THE DRAWINGS

Embodiments of the invention will now be described, by way of exampleonly, with reference to the accompanying schematic drawings in which:

FIG. 1 depicts a lithographic apparatus according to an embodiment ofthe invention;

FIG. 2 shows schematically the use of the lithographic apparatus of FIG.1 together with other apparatuses forming a production facility forsemiconductor devices, the facility including first and seconddiagnostic apparatus according to embodiments of the present invention;

FIGS. 3 and 4 illustrate the principles of advanced alignmentmeasurements and wafer grid corrections applied in a lithographicapparatus of the production facility;

FIG. 5 illustrates figuratively the combination of various“fingerprints” in an observed example of alignment measurements;

FIG. 6 shows the extraction of object data from alignment data by thefirst diagnostic apparatus in an embodiment of the invention;

FIGS. 7A and 7B show the form of object data in one embodiment of theinvention for two example product units, and FIG. 7C shows a simplifiedschematic representation of each product unit as a point or vector in amultidimensional space;

FIG. 8A shows the creation of a measurement data matrix comprisingobject data for a set of product units and FIG. 8B shows a schematicrepresentation of those product units as points in the multidimensionalspace;

FIGS. 9A, 9B, 9C and 9D illustrate steps in a multivariate analysis stepperformed by the first diagnostic apparatus to decompose thedistribution of object data represented in FIG. 8 into a plurality ofcomponent vectors;

FIGS. 10A, 10B and 10C illustrate distributions of product unitsprojected into one- and two-dimensional distributions using thecomponent vectors identified in the multivariate analysis;

FIG. 11A illustrates example “fingerprints” represented by componentvectors identified in the multivariate analysis and FIG. 11B illustratesthe projection of object data onto various two-dimensional spacesdefined by pairs of component vectors, such as may be displayed by thefirst or second diagnostic apparatus in an embodiment of the invention;

FIG. 12 is a flow chart summarizing steps in the operation of the firstand second diagnostic apparatus in an embodiment of the invention;

FIGS. 13 to 17 illustrate schematically various mode of operation of thesecond diagnostic apparatus that may be used independently or incombination for performing root cause analysis in an embodiment of theinvention;

FIG. 18 illustrates the correspondence between the measurements from aset of wafers and the elements of the vectors in an alternativeimplementation of a multivariate analysis;

FIG. 19 illustrates the principle of a performance monitoring functionin the production facility of FIG. 2;

FIG. 20 illustrates use of the component vectors identified in themultivariate analysis for reconstruction of high resolution object datafrom low resolution measurements in the performance monitoring function,according to another embodiment of the present invention;

FIG. 21 shows a diagram of a workflow of the performance monitoringfunction incorporating the reconstruction in the embodiment of FIG. 20;and

FIG. 22 illustrates schematically data processing hardware programmableto implement the first and/or second diagnostic apparatuses of theembodiments of the invention.

DETAILED DESCRIPTION OF EXEMPLARY EMBODIMENTS

FIG. 1 schematically depicts a lithographic apparatus LA according toone embodiment of the invention. The apparatus comprises:

-   -   an illumination system (illuminator) IL configured to condition        a radiation beam B (e.g. UV radiation or EUV radiation).    -   a support structure (e.g. a mask table) MT constructed to        support a patterning device (e.g. a mask) MA and connected to a        first positioner PM configured to accurately position the        patterning device in accordance with certain parameters;    -   a substrate table (e.g. a wafer table) WTa or WTb constructed to        hold a substrate (e.g. a resist-coated wafer) W and connected to        a second positioner PW configured to accurately position the        substrate in accordance with certain parameters; and    -   a projection system (e.g. a refractive projection lens system)        PS configured to project a pattern imparted to the radiation        beam B by patterning device MA onto a target portion C (e.g.        comprising one or more dies) of the substrate W.

The illumination system may include various types of optical components,such as refractive, reflective, magnetic, electromagnetic, electrostaticor other types of optical components, or any combination thereof, fordirecting, shaping, or controlling radiation.

The support structure supports, i.e. bears the weight of, the patterningdevice. It holds the patterning device in a manner that depends on theorientation of the patterning device, the design of the lithographicapparatus, and other conditions, such as for example whether or not thepatterning device is held in a vacuum environment. The support structurecan use mechanical, vacuum, electrostatic or other clamping techniquesto hold the patterning device. The support structure may be a frame or atable, for example, which may be fixed or movable as required. Thesupport structure may ensure that the patterning device is at a desiredposition, for example with respect to the projection system. Any use ofthe terms “reticle” or “mask” herein may be considered synonymous withthe more general term “patterning device.”

The term “patterning device” used herein should be broadly interpretedas referring to any device that can be used to impart a radiation beamwith a pattern in its cross-section such as to create a pattern in atarget portion of the substrate. It should be noted that the patternimparted to the radiation beam may not exactly correspond to the desiredpattern in the target portion of the substrate, for example if thepattern includes phase-shifting features or so called assist features.Generally, the pattern imparted to the radiation beam will correspond toa particular functional layer in a device being created in the targetportion, such as an integrated circuit.

The patterning device may be transmissive or reflective. Examples ofpatterning devices include masks, programmable mirror arrays, andprogrammable LCD panels. Masks are well known in lithography, andinclude mask types such as binary, alternating phase-shift, andattenuated phase-shift, as well as various hybrid mask types. An exampleof a programmable mirror array employs a matrix arrangement of smallmirrors, each of which can be individually tilted so as to reflect anincoming radiation beam in different directions. The tilted mirrorsimpart a pattern in a radiation beam which is reflected by the mirrormatrix.

The term “projection system” used herein should be broadly interpretedas encompassing any type of projection system, including refractive,reflective, catadioptric, magnetic, electromagnetic and electrostaticoptical systems, or any combination thereof, as appropriate for theexposure radiation being used, or for other factors such as the use ofan immersion liquid or the use of a vacuum. Any use of the term“projection lens” herein may be considered as synonymous with the moregeneral term “projection system”.

As here depicted, the apparatus is of a transmissive type (e.g.employing a transmissive mask). Alternatively, the apparatus may be of areflective type (e.g. employing a programmable mirror array of a type asreferred to above, or employing a reflective mask).

The lithographic apparatus may be of a type having two (dual stage) ormore substrate tables (and/or two or more mask tables). In such“multiple stage” machines the additional tables may be used in parallel,or preparatory steps may be carried out on one or more tables while oneor more other tables are being used for exposure. An embodiment of theinvention disclosed herein can be used in a stand-alone fashion, but inparticular it can provide additional functions in the pre-exposuremeasurement stage of either single- or multi-stage apparatuses.

The lithographic apparatus may also be of a type wherein at least aportion of the substrate may be covered by a liquid having a relativelyhigh refractive index, e.g. water, so as to fill a space between theprojection system and the substrate. An immersion liquid may also beapplied to other spaces in the lithographic apparatus, for example,between the mask and the projection system. Immersion techniques arewell known in the art for increasing the numerical aperture ofprojection systems. The term “immersion” as used herein does not meanthat a structure, such as a substrate, must be submerged in liquid, butrather only means that liquid is located between the projection systemand the substrate during exposure.

Illuminator IL receives a radiation beam from a radiation source SO. Thesource and the lithographic apparatus may be separate entities, forexample when the source is an excimer laser. In such cases, the sourceis not considered to form part of the lithographic apparatus and theradiation beam is passed from the source SO to the illuminator IL withthe aid of a beam delivery system BD comprising, for example, suitabledirecting mirrors and/or a beam expander. In other cases the source maybe an integral part of the lithographic apparatus, for example when thesource is a mercury lamp. The source SO and the illuminator IL, togetherwith the beam delivery system BD if required, may be referred to as aradiation system.

The illuminator IL may comprise an adjuster AD for adjusting the angularintensity distribution of the radiation beam. Generally, at least theouter and/or inner radial extent (commonly referred to as σ-outer andσ-inner, respectively) of the intensity distribution in a pupil plane ofthe illuminator can be adjusted. In addition, the illuminator IL maycomprise various other components, such as an integrator IN and acondenser CO. The illuminator may be used to condition the radiationbeam, to have a desired uniformity and intensity distribution in itscross-section.

The radiation beam B is incident on the patterning device (e.g., maskMA), which is held on the support structure (e.g., mask table MT), andis patterned by the patterning device. Having traversed the mask MA, theradiation beam B passes through the projection system PS, which focusesthe beam onto a target portion C of the substrate W. With the aid of thesecond positioner PW and position sensor IF (e.g. an interferometricdevice, linear encoder or capacitive sensor), the substrate tableWTa/WTb can be moved accurately, e.g. so as to position different targetportions C in the path of the radiation beam B. Similarly, the firstpositioner PM and another position sensor (which is not explicitlydepicted in FIG. 1) can be used to accurately position the mask MA withrespect to the path of the radiation beam B, e.g. after mechanicalretrieval from a mask library, or during a scan. In general, movement ofthe mask table MT may be realized with the aid of a long-stroke module(coarse positioning) and a short-stroke module (fine positioning), whichform part of the first positioner PM. Similarly, movement of thesubstrate table WTa/WTb may be realized using a long-stroke module and ashort-stroke module, which form part of the second positioner PW. In thecase of a stepper (as opposed to a scanner) the mask table MT may beconnected to a short-stroke actuator only, or may be fixed. Mask MA andsubstrate W may be aligned using mask alignment marks M1, M2 andsubstrate alignment marks P1, P2. Although the substrate alignment marksas illustrated occupy dedicated target portions, they may be located inspaces between target portions (these are known as scribe-lane alignmentmarks). Similarly, in situations in which more than one die is providedon the mask MA, the mask alignment marks may be located between thedies.

The depicted apparatus could be used in at least one of the followingmodes:

1. In step mode, the mask table MT and the substrate table WTa/WTb arekept essentially stationary, while an entire pattern imparted to theradiation beam is projected onto a target portion C at one time (i.e. asingle static exposure). The substrate table WTa/WTb is then shifted inthe X and/or Y direction so that a different target portion C can beexposed. In step mode, the maximum size of the exposure field limits thesize of the target portion C imaged in a single static exposure.2. In scan mode, the mask table MT and the substrate table WTa/WTb arescanned synchronously while a pattern imparted to the radiation beam isprojected onto a target portion C (i.e. a single dynamic exposure). Thevelocity and direction of the substrate table WTa/WTb relative to themask table MT may be determined by the (de-)magnification and imagereversal characteristics of the projection system PS. In scan mode, themaximum size of the exposure field limits the width (in the non-scanningdirection) of the target portion in a single dynamic exposure, whereasthe length of the scanning motion determines the height (in the scanningdirection) of the target portion.3. In another mode, the mask table MT is kept essentially stationaryholding a programmable patterning device, and the substrate tableWTa/WTb is moved or scanned while a pattern imparted to the radiationbeam is projected onto a target portion C. In this mode, generally apulsed radiation source is employed and the programmable patterningdevice is updated as required after each movement of the substrate tableWTa/WTb or in between successive radiation pulses during a scan. Thismode of operation can be readily applied to maskless lithography thatutilizes programmable patterning device, such as a programmable mirrorarray of a type as referred to above.

Combinations and/or variations on the above described modes of use orentirely different modes of use may also be employed.

Lithographic apparatus LA in this example is of a so-called dual stagetype which has two substrate tables WTa and WTb and two stations—anexposure station and a measurement station—between which the substratetables can be exchanged. While one substrate on one substrate table isbeing exposed at the exposure station EXP, another substrate can beloaded onto the other substrate table at the measurement station MEA sothat various preparatory steps may be carried out. The preparatory stepsmay include mapping the surface height of the substrate using a levelsensor LS and measuring the position of alignment marks on the substrateusing an alignment sensor AS. The alignment marks are arranged nominallyin a regular grid pattern. However, due to inaccuracies in creating themarks and also due to deformations of the substrate that occurthroughout its processing, the marks deviate from the ideal grid.Consequently, in addition to measuring position and orientation of thesubstrate, the alignment sensor in practice must measure in detail thepositions of many marks across the substrate area, if the apparatus LAis to print product features at the correct locations with very highaccuracy. The measurement of alignment marks is therefore verytime-consuming and the provision of two substrate tables enables asubstantial increase in the throughput of the apparatus. If the positionsensor IF is not capable of measuring the position of the substratetable while it is at the measurement station as well as at the exposurestation, a second position sensor may be provided to enable thepositions of the substrate table to be tracked at both stations. Anembodiment of the invention can be applied in an apparatus with only onesubstrate table, or with more than two.

The apparatus further includes a lithographic apparatus control unitLACU which controls all the movements and measurements of the variousactuators and sensors described. LACU also includes signal processingand data processing capacity to implement desired calculations relevantto the operation of the apparatus. In practice, control unit LACU willbe realized as a system of many sub-units, each handling the real-timedata acquisition, processing and control of a subsystem or componentwithin the apparatus. For example, one processing subsystem may bededicated to servo control of the substrate positioner PW. Separateunits may even handle coarse and fine actuators, or different axes.Another unit might be dedicated to the readout of the position sensorIF. Overall control of the apparatus may be controlled by a centralprocessing unit, communicating with these sub-systems processing units,with operators and with other apparatuses involved in the lithographicmanufacturing process.

FIG. 2 at 200 shows the lithographic apparatus LA in the context of anindustrial production facility for semiconductor products. Within thelithographic apparatus (or “litho tool” 200 for short), the measurementstation MEA is shown at 202 and the exposure station EXP is shown at204. The control unit LACU is shown at 206. Within the productionfacility, apparatus 200 forms part of a “litho cell” or “litho cluster”that contains also a coating apparatus 208 for applying photosensitiveresist and other coatings to substrate W for patterning by the apparatus200. At the output side of apparatus 200, a baking apparatus 210 anddeveloping apparatus 212 are provided for developing the exposed patterninto a physical resist pattern.

Once the pattern has been applied and developed, patterned substrates220 are transferred to other processing apparatuses such as areillustrated at 222, 224, 226. A wide range of processing steps areimplemented by various apparatuses in a typical manufacturing facility.For the sake of example, apparatus 222 in this embodiment is an etchingstation, and apparatus 224 performs a post-etch annealing step. Furtherphysical and/or chemical processing steps are applied in furtherapparatuses, 226, etc. Numerous types of operation can be required tomake a real device, such as deposition of material, modification ofsurface material characteristics (oxidation, doping, ion implantationetc.), chemical-mechanical polishing (CMP), and so forth. The apparatus226 may, in practice, represent a series of different processing stepsperformed in one or more apparatuses.

As is well known, the manufacture of semiconductor devices involves manyrepetitions of such processing, to build up device structures withappropriate materials and patterns, layer-by-layer on the substrate.Accordingly, substrates 230 arriving at the litho cluster may be newlyprepared substrates, or they may be substrates that have been processedpreviously in this cluster or in another apparatus entirely. Similarly,depending on the required processing, substrates 232 on leavingapparatus 226 may be returned for a subsequent patterning operation inthe same litho cluster, they may be destined for patterning operationsin a different cluster, or they may be finished products to be sent fordicing and packaging.

Each layer of the product structure requires a different set of processsteps, and the apparatuses 226 used at each layer may be completelydifferent in type. Further, even where the processing steps to beapplied by the apparatus 226 are nominally the same, in a largefacility, there may be several supposedly identical machines working inparallel to perform the step 226 on different substrates. Smalldifferences in set-up or faults between these machines can mean thatthey influence different substrates in different ways. Even steps thatare relatively common to each layer, such as etching (apparatus 222) maybe implemented by several etching apparatuses that are nominallyidentical but working in parallel to maximize throughput. In practice,moreover, different layers require different etch processes, for examplechemical etches, plasma etches, according to the details of the materialto be etched, and special requirements such as, for example, anisotropicetching.

The previous and/or subsequent processes may be performed in otherlithography apparatuses, as just mentioned, and may even be performed indifferent types of lithography apparatus. For example, some layers inthe device manufacturing process which are very demanding in parameterssuch as resolution and overlay may be performed in a more advancedlithography tool than other layers that are less demanding. Thereforesome layers may be exposed in an immersion type lithography tool, whileothers are exposed in a ‘dry’ tool. Some layers may be exposed in a toolworking at DUV wavelengths, while others are exposed using EUVwavelength radiation.

Also shown in FIG. 2 is a metrology apparatus 240 which is provided formaking measurements of parameters of the products at desired stages inthe manufacturing process. A common example of a metrology station in amodern lithographic production facility is a scatterometer, for examplean angle-resolved scatterometer or a spectroscopic scatterometer, and itmay be applied to measure properties of the developed substrates at 220prior to etching in the apparatus 222. Using metrology apparatus 240, itmay be determined, for example, that important performance parameterssuch as overlay or critical dimension (CD) do not meet specifiedaccuracy requirements in the developed resist. Prior to the etchingstep, the opportunity exists to strip the developed resist and reprocessthe substrates 220 through the litho cluster. As is also well known, themetrology results from the apparatus 240 can be used for qualitycontrol. They can also be used as inputs for a process monitoringsystem. This system can be to maintain accurate performance of thepatterning operations in the litho cluster, by making small adjustmentsover time, thereby minimizing the risk of products being madeout-of-specification, and requiring re-work. Of course, metrologyapparatus 240 and/or other metrology apparatuses (not shown) can beapplied to measure properties of the processed substrates 232, 234, andincoming substrates 230.

In order to provide tools for use in analyzing the sources of poorperformance in lithographic production systems, there is now disclosedthe provision of diagnostic apparatus 250 and 252, as illustrated at thetop of FIG. 2. Similar tools in another form can be used to improveperformance of the process monitoring system, as will also be described.

Each diagnostic apparatus 250, 252 is implemented by a combination ofcomputer hardware and software, connected to receive data from themanufacturing facility just described. The computer hardware can belocated in the same facility as the litho tool and other apparatus, orit can be located remotely and connected by telecommunications channelsand/or removable storage. As will be explained, apparatus 250 and 252can produce, for example, a report 254 identifying a likely cause, or alist of potential causes, for an identified error. It may produceready-made corrections 256, which can be applied to the control systemsof one or more of the apparatuses 200-226, to improve the performance ofthe system in processing product units in future. Corrections may beassociated with context criteria indicating that they should be appliedselectively to product units, depending on their individual processinghistory.

The first diagnostic apparatus 250 is designed to perform multivariateanalysis, for example principal component analysis (PCA), to identify anumber of component vectors contributing to deviations measured from theproducts themselves (substrates in this case). Different forms ofmultivariate analysis may be used, and PCA analysis is referred toherein purely as one example. In the specific example case of PCA, theidentified component vectors are eigenvectors of a covariance matrix ofthe measurement data. The component vectors are orthogonal in themultidimensional space. In another method, called Independent ComponentAnalysis (ICA), projections of the measurement data onto the componentvectors are as independent as possible. The ICA technique leaves allsecond and higher order cross-correlations at zero, while theorthogonality of the PCA technique forces second ordercross-correlations to be zero but may leave non-zero higher ordercross-correlations. Apparatus 250 will be referred to hereinafter as thePCA apparatus for convenience, without intending any limitation.

Input for PCA apparatus 250 is object data, that is data measured on theproduct units themselves. In the particular embodiment illustrated anddescribed herein, the object data, stored in a database 260 comprises inparticular the alignment data conventionally obtained by thelithographic apparatus 200 using the alignment sensors AS in themeasurement station 202. As this data representing detailed measurementsof positions of marks in the X-Y plane of the substrate is obtainedinherently as part of the normal patterning operation, little or nopenalty is incurred by instructing the control unit 206 to store thedata in the object data storage 260. In other embodiments, the objectdata may be measured elsewhere in the system, in addition to or insteadof the alignment data measured by the litho tool 200. Alternatively orin addition to the alignment data, the object data may include heightdata obtained using level sensor LS, “wafer quality” signals from thealignment sensors AS and the like. The object data in storage 260 mayalso be obtained from other measurement apparatus, for example themetrology apparatus 240. In this way, the object data can includemeasurements directly or indirectly of parameters such as overlay, CD,side wall angle, mark asymmetry, leveling and focus. Further below, anembodiment will be described in which such object data can be used andanalyzed to implement an improved process monitoring system in themanufacturing facility of FIG. 2. It is also possible that theseparameters can be measured by apparatus within the litho tool 200itself. Various prior publications describe special marks and/or ormeasurement techniques for this. For example information on markasymmetry can be obtained using signals obtained at differentwavelengths by the alignment sensors.

The second diagnostic apparatus 252 is for performing root causeanalysis (RCA), for establishing correlation between component vectorsidentified by the PCA apparatus and performance and/or context dataassociated with individual substrates. This RCA apparatus 252 isarranged to receive the results of the multivariate analysis from PCAapparatus 250. RCA apparatus 252 then correlates the observed componentvectors based on the object data alone, with one or more items of whatwe shall call context data and performance data. This context data mayalso be regarded as “history” data, as it is data not obtained from theproducts themselves but representing all or part of the processinghistory of individual product units (substrates), or batches of productunits. Arrows 262 throughout the diagram illustrate how context data maycome from any of the apparatuses. Context data may also arrive with thenew substrates 230. For example, the context data may record what typesof process steps have been applied, which individual apparatuses havebeen used in the performance of those steps, and what parameters wereapplied by those apparatuses (for example settings of temperature orpressure case while in etching apparatus 222, or parameters such asillumination modes, alignment recipes, etc. in the litho tool 200). Thecontext data is stored in storage 264 for use by the RCA apparatus 252.

RCA apparatus 252 further has access to performance data, which mayinclude for example measurements of overlay or CD, and which is storedin storage 266. While FIG. 2 shows separate storage 260, 264, 266 foreach of the object data, context data and performance data, it will beappreciated that these different types of data may be stored in onecommon storage unit, or may be distributed over a larger number ofstorage units, from which particular items of data can be retrieved whenrequired. Further, whilst the context data 262 is shown as emanatingfrom each individual apparatus 222, 224, etc. the data may be collectedthrough a central control system that controls the operation of themanufacturing plant as a whole.

Each record in the object data storage is labeled with a uniqueidentifier. Noting that an individual wafer might pass repeatedlythrough the same litho tool in the course of a manufacturing process, ormight pass through different tools all measuring the same marks, it ispossible collect object data for the same product unit at differentstages of the manufacturing process. Each of these instances ofmeasurement can be treated in the analysis as an independent productunit. In the case where there are multiple instances of the same waferbeing measured at different stages in a complex manufacturing process,however, the object data will include an identifier that uniquelyidentifies not only the individual wafer, but the stage of processing inwhich it has been measured. Typically in a lithographic process,different instances of the same wafer will be associated with patterningsuccessive layers of a device structure. Knowledge of the relationshipbetween these instances in the object data can be used as context datafor diagnostic purposes in the RCA apparatus 252.

As the multivariate analysis in first diagnostic apparatus 250 can beperformed independently of the context data, that apparatus can operateindependently of the availability of any particular form or completenessof context data. However, context data can also be used by the firstdiagnostic apparatus if desired, for example to select certain subsetsof the product units for inclusion in the data for multivariateanalysis, rather than differentiating between product units only whenthe results of the multivariate analysis are displayed. As examples,so-called “chuck-to-chuck” comparisons can be important in a case wherethe litho tool has more than one “chuck” or substrate table (WTa, WTb inFIG. 1). When it has access to this part of the context data, the PCAapparatus 250 can select and analyze separately the product units thathave been processed on the different chucks. The multivariate analysismay be performed so as to discriminate between subsets of product unitswithout treating them entirely separately. Methods such as the one knownas “mixtures of PCA” allow the analysis to be performed with regard tocertain clusters within the object data, without explicitly separatingtheir datasets. Instead, the different analyses per cluster are weightedwith the likelihood that a certain vector (corresponding to a certainmeasured product unit) falls within a certain cluster.

In general, then, the multivariate analysis can be performed in a mannerthat discriminates between subsets of vectors at least partially byreference to context data. The context data may identify a particularapparatus or part of an apparatus involved in processing the productunits, as in chuck-to-chuck comparison. The context data may a stage(step) in the industrial process at which the measurements representedin the vectors were obtained, as for example in layer-to-layercomparison.

Storage 268 is provided for library data which can be used forrecognizing patterns in the results of the multivariate analysis. Inparticular, it has been mentioned already that certain fingerprint typescan be recognized by experts familiar with the process, and thisrecognition brings with it certain knowledge of likely causes andeffects. The library data can store a collection of reference vectorsthat can be matched with vectors identified from the object data. Once areference vector has been matched, further information stored inassociation with it can be retrieved from storage and used to guide thefurther operation of PCA apparatus 250 and/or RCA apparatus 252. Forexample, the data stored with a “swirl” fingerprint in the library mightcomprise the name label “swirl” and hints to look for correlationbetween this fingerprint and annealing operations in the context datafor the affected product units.

Object Data Example: Litho Tool Alignment Data

As explained above, the diagnostic methods and apparatus disclosedherein employ object data that is data measured from points distributedspatially over each product unit. In the example of a lithographicproduction facility where the product units are semiconductor substrates(wafers), a particularly interesting source of comprehensive object datais the set of measurements performed in the litho tool to characterizeeach wafer and the patterns previously deposited upon it. Thesemeasurements are used to obtain parameters for alignment models, thatare used in a new patterning step to control accurately the positioningof patterns applied in relation to features already present

Standard alignment models have six parameters (effectively three perdirection X & Y) and in addition there are more advanced alignmentmodels. On the other hand, for the most demanding processes currently inuse and under development, to achieve the desired overlay performancerequires more detailed corrections of the wafer grid. While standardmodels might use fewer than ten parameters, advanced alignment modelstypically use more than 15 parameters, or more than 30 parameters.Examples of advanced models are higher order wafer alignment (HOWA)models, zone-alignment (ZA) and radial basis function (RBF) basedalignment models. HOWA is a published technique based on second, thirdand higher order polynomial functions. Zone alignment is described forexample in Huang et al, “Overlay improvement by zone alignmentstrategy”, Proc. SPIE 6922, 69221G (2008). RBF modeling is described inpublished patent application US 2012/0218533. Different versions andextensions of these advanced models can be devised. The advanced modelsgenerate a complex description of the wafer grid that is corrected for,during the exposure of the target layer. RBF and latest versions of HOWAprovide particularly complex descriptions based on tens of parameters.This implies a great many measurements are required to obtain a wafergrid with sufficient detail. FIGS. 3 & 4 illustrate the form ofalignment information that can be used to correct for wafer griddistortion as measured by the alignment sensor AL on alignment marks(targets) 400 in a previous layer on wafer (substrate) W. Each targethas a nominal position, defined usually in relation to a regular,rectangular grid 402 with axes X and Y. Measurements of the realposition 404 of each target reveal deviations from the nominal grid. Thealignment marks may be provided within device areas of the substrate,and/or they may be provided in so-called “scribe lane” areas betweendevice areas.

As illustrated in FIG. 4 the measured positions 404 of all the targetscan be processed numerically to set up a model of a distorted wafer grid406 for this particular wafer. This alignment model is used in thepatterning operation to control the position of the patterns applied tothe substrate. In the example illustrated, the straight lines of thenominal grid have become curves, indicating use of a higher order(advanced) alignment model. It goes without saying that the distortionsillustrated are exaggerated compared to the real situation. Alignment isa unique part of the lithographic process, because it is the correctionmechanism able to correct for deviations (distortions) in each exposedwafer. The alignment measures positions of alignment targets formed in aprevious layer. The inventors have recognized that alignment data (andrelated data such as level sensor data) is always collected and alwaysavailable. By finding a way to exploit this data as a resource for usein root cause analysis, the methods and apparatuses described hereingreatly increase the practicality of such analysis.

First Diagnostic Apparatus—Background

FIG. 5 illustrates at 500, a very simple illustration of alignment datathat may be measured across a substrate at the measurement station 202of the litho tool 200. Each small arrow represents the position andmagnitude of a mark position measured by the alignment sensor AS,relative to a nominal position, for a particular mark on the substrate.The collection of positional deviations measured at points spatiallydistributed over the wafer is an example of object data for oneparticular product unit. All the product units have the same spatialdistribution of marks and measurements, but the actual deviations aregenerally unique to each wafer. Analysis of the object data (wafermeasurements) over a population of product units can be performed so asto reveal various “fingerprints” that may be hidden in the data. It isknown that any of the different steps in the production of the processedsubstrate can contribute its own fingerprint to the distribution ofposition errors across the substrate. At 510, there are shown fourexample contributions. The first contribution known as writing error,comes from errors the patterning device (reticle) MA. The writing errorand may also include distortions caused by the reticle. Anothercontribution of error is in the operation of the litho tool LA. In thisexample, the deviations are small and alternate in alternating fields,illustrating a typical “scan up, scan down” (SUSD) error distribution.These errors, that may be referred to in lithography as the “machinefingerprint” are distributed with a relatively high spatial frequencyacross the substrate.

Further contributions to the wafer measurements are so-called “processfingerprints” that arise from processing steps performed outside thelitho tool. The third contribution illustrated in FIG. 3 is a typicalpattern of distortion suffered by the product in the etching apparatus222. Errors are generally aligned radially, and are larger towards theperiphery of the substrate. This type of pattern resembles a “sombrero”pattern. A fourth type of fingerprint illustrated in FIG. 3 is a socalled “dual swirl” pattern, such as may be imposed in a thermalannealing step, for example in the apparatus 224. When a substrate hasbeen subjected to these different steps, and is subsequently reloadedand measured in the litho tool measurement station 202, or in anymetrology apparatus, a complex pattern of position errors that is acombination of all these different fingerprints may be observed, asshown at 500. Bearing in mind that a real product may have gone throughdozens of process steps, including many cycles of patterning andprocessing in different apparatuses and different types of apparatuses,it becomes very difficult to know which types of apparatus, let alonewhich individual apparatuses, have contributed to errors present in thefinished product. The contributions of these additional processingcycles are illustrated schematically at 512, 514, etc. Moreover, thefact that one of these characteristic fingerprints is strongly presentin the object data does not necessarily indicate a strong source oferror. For example, the litho tool SUSD fingerprint may be presentstrongly without contributing anything to overlay error, if the sametool or a tool having a similar fingerprint is used to patternsubsequent layers.

The PCA apparatus 250 exploits the availability of such object datastored for many individual product units (wafers) to extract usefulinformation in an automated fashion. Component vectors are identified,each component vector corresponding to one of the fingerprints presentin the object data. Operation of the PCA apparatus does not depend onthe availability of context data or even performance data. The RCAapparatus 252 is optional according to the present disclosure, but canbe used where context data is available, to analyze the context datatogether with the PCA analysis results, to further identify suspectapparatuses and opportunities for process improvement. Operation of RCAapparatus can be by a mixture of automated and manual steps.

FIG. 6 illustrates the collection of object data in the embodiment ofFIG. 2, during performance of a patterning operation by litho tool 200.As already described, measurement station 202 of the litho tool 200 usesalignment sensors AS to measure positional deviations 404 of individualmarks, spatially distributed across the substrate W. As mentioned abovewith reference to FIGS. 4 and 5, alignment models used in lithographycan be of low order or high order (advanced) type. In the presentexample, a higher order correction module 602 calculates an alignmentmodel 406 according to the HOWA method, mentioned above. This alignmentmodel is used at the exposure station 204 to apply a pattern tosubstrate. For the purposes of the PCA apparatus 250, we propose to useresidual data, rather than the deviations 404 as measured by thealignment sensors. This is because, in a modern high-performancelithography apparatus, most of the measured deviation will becompensated by the alignment model. Therefore performance improvementsand diagnostic methods concentrate on detecting and eliminating thesmall deviations that remain uncorrected by the model. One option wouldtherefore be to use as the object data, residual deviations that are notcorrected by the HOWA model. In the present example, however, thedesigners have made a different choice.

In the present embodiment it is chosen to use residuals aftersubtraction of only a low order correction, so that high orderdeviations, even though some of them may be compensated by the HOWAmodel in operation of the litho tool, are nevertheless revealed in theobject data. Leaving high order deviations in the residuals mayfacilitate diagnostic interpretation of the resulting component vectors.The HOWA model corrects low order and high order deviationssimultaneously. To make a low order correction accessible forcalculation of residuals, in the present embodiment, a traditional6-parameter (6 PAR) model 402′ is separately calculated by a unit 604.The 6 PAR calculating unit calculating unit 604 may be provided alreadyas part of the litho tool management software, or it may be providedspecially as part of the diagnostic apparatus. The low order model 402′is subtracted from the measured deviations 404 to obtain residualdeviations 404′. These residual variations 404′ are collected as theobject data for use in the PCA apparatus 250. In embodiments using adifferent higher order model, or no higher order model at all, the 6PARcalculation unit 604 may be provided already, and the residuals 404′ maybe calculated already. For example, the RBF model described in the priorart mentioned above, is generally applied to correct only the higherorder deviations, after low order deviations have been corrected by alow order model such as the 6PAR model.

In other embodiments, for example, where level sensor (LS) data is used,the deviations may again be used as object data, after subtraction ofsome corrective model, depending on which fingerprints are of mostinterest. In applications outside lithography, similar considerationscan be applied to determine the best form of object data upon which tobase the analysis.

Fingerprint Decomposition

FIGS. 7-9 illustrate steps in the analysis performed by the firstdiagnostic apparatus in the example embodiment. In FIG. 7A, we show therepresentation of the residual deviations on a first substrate W(1) as avector AL(1). Each measured deviation has x and y components. It isassumed that each wafer has n alignment marks to be measured (or atleast, for the purposes of this analysis, residual deviations for nmarks are collected in the object data). The x deviation for the firstmark on wafer number 1 is labeled x_(1,1), while the x deviation for then-th mark on the first substrate is labeled x_(1,n). The vector AL(1)comprises all the x and y values for the marks on the first substrate.Similarly, as shown in FIG. 7B, the residual deviations for a secondwafer W(2) are stored as a vector AL(2). The components of this vectorare the residual deviations for the n marks as measured on the secondwafer, with labels x_(2,1) to x_(2,n) and y_(2,1) to y_(2,n). In analternative implementation, the data can be organized into a vector permark position, that is to say a vector X(1) would comprise the first xvalue for all the wafers, a wafer X(2) would comprise the second x valuefor all the wafers and so forth. The alternative implementation will beexplained in a separate section, further below.

FIG. 7C illustrates how the “position” of each product unit (wafer)W(1), W(2), etc. can be plotted in a multidimensional space, having asmany dimensions as there are elements in the vectors AL(1), AL(2), etc.In view of the limitations of representing a multidimensional space in aflat drawing, FIG. 7C represents only the first three dimensions, namelythe residual deviations in the x direction for the first three marks oneach substrate.

Referring now to FIG. 8A, it is seen how the vectors comprising theresidual deviations for a full set of m wafers can be assembled into asingle matrix AL(1-m). It will be appreciated that the dimensions ofthis matrix may be several hundred rows and several hundred columns,depending on the number n of marks measured per wafer and the number mof wafers included in the analysis.

FIG. 8B, this shows again how each product unit W(i) can be representedby a point defined by its vector AL(i) in the multidimensional space.This is possible because corresponding elements of the vector AL(i) ofeach wafer correspond to the same location in the spatial distributionof measurement points (alignment marks) on the product units (wafers).In an ideal production situation, all wafers would naturally bepositioned on the origin O, with zero positional deviation at any mark.In a real situation, although they are distributed away from the originO, but they are not randomly distributed throughout the multidimensionalspace. Rather, as shown schematically in FIG. 8B, the pointsrepresenting the ends of the individual vectors AL(i) will bedistributed with some degree of coherence, for example with a number ofclusters being recognizable, and one or more “outliers”, in a typicaldistribution. On the other hand, while these clusters are visible in theschematic, three-dimensional plot of FIG. 8B, they are not readilyidentifiable when buried in a hundred-or more dimensional space.

FIGS. 9A and 9B show how the first diagnostic apparatus, the PCAapparatus 250 of the disclosed apparatus decomposes the multidimensionaldistribution of vectors into component vectors, referred also to asfingerprints. For this purpose, various techniques are known inmultivariate statistics that can be applied, whether individually or incombination, to extract a set of component vectors from the mass of datarepresented in the object data.

In the step illustrated at FIG. 9A, there is calculated an averagevector AL(avg) representing the average of all the vectors AL(1) toAL(m) represented in the object data. At FIG. 9B, the origin of themultidimensional space is shifted by subtracting the average vector fromeach of the vectors expressed in the original multidimensional space.This can be seen by the relabeling of the axes in FIG. 9B with x′instead of x. It will be understood that this shifting of the origin Oto a new position O′ is a mathematical step that can be implemented byactually subtracting the average vector from the individual vectorswhere they are stored, or by applying an offset when the values are usedin calculation. The values can be normalized to an arbitrary scale, ifdesired.

The result after the step of FIG. 9B is a measurement matrix AL(1-m) ofdimension 2n×m in which the columns are individual vectors relative tothe new origin O′. PCA apparatus computes from this matrix a datacovariance matrix. Using conventional notation, covariance matrix isdesignated Σ and has dimension 2n×2n and has entries:

Σ_(i,j) =E[(α_(i)−μ_(i))(α_(j)−μ_(j))]

where Σ_(i,j) is the entry in row i, column j of the matrix, α_(i) andα_(j) are the i^(th) and j^(th) rows of entries in the measurementmatrix (for example α₁=[x_(1,1) . . . x_(1,m)], α_(2n)=[y_(n,1) . . .y_(n,m)]), E(α_(i)−μ_(i)) is the expectation of the entries in alrelative to the mean of those entries and E(α_(j)−α_(j)) is theexpectation of the entries in α_(j) relative to the mean of thoseentries. (Note that, if the values in the measurement matrix havealready been adjusted be relative to the mean, as shown in FIG. 9, thenthe terms E(α_(i)−μ_(i)) and E(α_(j)−μ_(j)) can be simplified toE(α_(i)) and E(α_(j)).) Using a compact matrix notation, the covariancematrix can be expressed as:

Σ=E[AL(1−m)*AL(1−m)^(T)]

where superscript T indicates the transpose operator. As an alternativeto a covariance matrix, a correlation matrix can be calculated. Thedifference is simply that correlation values have been normalized to arange from 0 (uncorrelated) to 1 (completely correlated).

The PCA apparatus then exploits the spatial correlation betweenalignment errors in different targets or marks to project the data ontoeigenvectors of the covariance matrix. These eigenvectors are an exampleof the component vectors mentioned in the introduction and claims. Theseeigenvectors can be interpreted as representing wafer-to-waferfingerprints that contribute to the overall fingerprint of each wafer.Principal component analysis or PCA is one known decomposition techniqueby which this decomposition into component vectors can be performed.Some other forms of decomposition may be also of interest to use, aswill be mentioned. The references to principal component vectors and PCAanalysis in the present description should be interpreted broadly toencompass these various alternative decomposition techniques, unless thecontext requires otherwise.

FIG. 9C illustrates a first component vector PC1 which has been found byPCA analysis of the covariance matrix illustrated in FIG. 8A. Thisvector PC1 emerges from the calculations and can be understoodqualitatively as the single vector which captures the most variance ofthe measured points in the multidimensional space. In other words, eachmeasured vector can be represented (very approximately) by a scalarcoefficient times first component vector. In the present case, sincemost of the measured vectors fall in two clusters 900 and 904, thedirection of component vector PC1 is unsurprisingly aligned so as topass through these two clusters, while being influenced also by thesmaller cluster 902 and the outlier 906. A next component vector PC2 isdefined, as illustrated in FIG. 9D. Each component vector PC1, PC2, etc.is defined as the one which captures the most variance of thedistribution of points in the object data, after subtracting from eachpoint the approximation represented in terms of the vector or vectorsalready identified. The component vectors in the PCA process areorthogonal, as indicated at 908. The process continues until asufficient number of component vectors have been identified, butwhatever measured is set by the designer and operator of the apparatus.Note that, while the finding of these component vectors has beendescribed as an iterative process, finding and subtracting eachcomponent vector in turn, for practical implementations both paralleland sequential methods are available.

If the points in the multidimensional space were distributed entirely atrandom, the number of component vectors required to describe thedistribution with sufficient accuracy would hardly be fewer than 2n, thenumber of elements in each measurement vector. However, in a real dataset there is a high degree of spatial coherence in the deviations orother measurements distributed across the wafer. Therefore substantialcorrelations between entries are expected, and it is found that thedistribution can be very well described as a combination of relativelyfew component vectors. Another term for this process of finding thecomponent vectors is therefore dimensionality reduction. Moreover, thesecomponent vectors may be expected to have a fairly direct relationshipwith physical effects in the manufacturing process, and thereby offerkeys to finding the cause of problems. Based on the decomposition thathas been illustrated schematically in FIG. 9, the first diagnosticapparatus 250 can deliver a set of component vectors, onto which themeasured vector of each product unit can be projected for analyticpurposes.

It should be noted that the measurements used as object data in themultivariate analysis may be only a subset of the measurements taken andavailable. There are various reasons for selecting only certainmeasurements. One reason is simply to reduce the amount of dataprocessing required. More particularly, if one wants to analyze patternsacross the whole wafer, one could restrict the analysis to an interfieldsubset of marks, that is one mark per field, covering the full wafer(“field” is a term for the target portions C of FIG. 1). Conversely, toanalyze intrafield patterns, a subset of measurements may be ones takenfrom only a few fields, but with several marks distributed across eachfield. Another example would be a subset specifically relating to onelayer in one product type; other subsets relate to other layers andother products. Multivariate analysis can be done separately on eachsubset so that the database is relevant to each litho step.

It should be noted that performing the multivariate analysis aftersubtracting an average vector is only one possible implementation. Also,performing the multivariate analysis using a covariance matrix is onlyone possible implementation. Other choices are possible, as is known inthe art of PCA techniques and multivariate analysis generally.

Further the decision to combine all x and y mark positions into onevector is merely one design option. The different coordinates x and ycould be treated entirely separately, if preferred.

FIG. 10 illustrates how projections onto various ones of the componentvector axes can be used to identify product units of interest. FIG. 10Aillustrates the projection onto an axis represented by the firstcomponent vector PC1. We see how the vector AL(i) of each product unitin the multidimensional space is reduced a single-dimensional value,namely the coefficient c(PC1). Comparing roughly with the distributionsseen in three dimensions in FIG. 9, the clusters 900 to 904 arerecognizable, as well as the outlier 906. Applying a statisticalthreshold to this distribution allows outliers such as point 906 to beidentified. For example, 910 in the drawing indicates a Gaussiandistribution curve that has been fitted to the data, with its meancentered on the mean value of the coefficient c(PC1). Statisticalsignificance thresholds can be established, as indicated at 912, 914.Point 906 and point 916 lie outside these thresholds, and are identifiedas being of interest.

Points identified as being of interest will be distinguished by theirblack color in this drawing and the following drawings, in contrast tothe open circles used for other points. The open and closed circles usedherein are merely to present a very simple example, and one that iscompatible with the requirements of patent drawings. In a user interfaceof PCA apparatus 250 and RCA apparatus 252 in a practical embodiment,similar markings, and also flags, color coding, different shapes and thelike can be used to distinguish many different subsets of the wafers.While for the present description we assume that each plotted pointrepresents an individual product unit (such as a semiconductor wafer),the apparatus may also allow data from multiple product units to beaggregated and plotted as a single point. As an example, data for wafersin each lot (production batch) can be averaged and plotted as a singlepoint representing the lot. This may facilitate visualization andanalysis of lot-to-lot variations, on occasions where the plotting ofall individual product units would be too cluttered. The user interfaceof the apparatus can provide simple controls for the user to switch onor off different types of aggregation. Aggregation can in principle beperformed prior to performing the multivariate analysis, but this wouldbe at the expense of “burying” information relating to individualoutlying product units.

FIG. 10B shows similarly the distribution of the same population ofpoints when projected onto a second axis defined by the second componentvector PC2, identified by the multivariate analysis. In this view, theclusters 900-904, as well as outlier 906 all lie in a central region,inside the thresholds 920, 922 defined by the fitted Gaussian curve 924.The point 916 lies outside the thresholds, and is therefore flagged asbeing of interest. On this projection, however, point 906 does not lieoutside the thresholds. It may be flagged as being of interest manually,or by transferring the designation “of interest” from another step inthe analysis, but it will not be flagged automatically by thestatistical analysis on component vector PC2, illustrated in FIG. 10B.It will be understood that such statistical calculations can beautomated within the PCA apparatus 250 and/or RCA apparatus 252, while adegree of manual selection/de-selection can also be provided for. Thethresholds and distribution curves used to identify points of interestcan be user-configurable. For example, values of sigma, 3-sigma,6-sigma, etc. can be used.

In FIG. 10C, additional information can be obtained by plotting theproduct units against two or more of the identified component vectors.In this illustration, a 2-dimensional plot is shown, with axescorresponding to the coefficients of component vectors PC1 and PC2, thatwere illustrated in FIGS. 10A and 10B. This illustration, which maycorrespond to a printed or displayed report of the apparatus 250,effectively projects all the points in the multidimensional space onto aplane defined by the two component vectors PC1, PC2. Similarly, for 3Dvisualization, projection may be performed into a 3-dimensional spacedefined by three component vectors. A user interface may provide a 3Ddisplay for this. Whether the number of dimensions is two, three, fouror more, this projection may be regarded as projection onto a plane orhyperplane that is a small subset of the many dimensions in themultidimensional space. Looking at the 2-D plot in FIG. 10C, theapparatus applies automated statistical techniques, and/or facilitatesuse of manual observation and selection, to define a threshold 930,outside which points will be considered points of interest forinvestigation. Compared with the 1-dimensional views seen at FIGS. 10Aand 10B, it can be seen that outliers 906 and 916 are more readilyidentified than in the 1D plots.

FIG. 11A illustrates examples of component vectors numbers 1, 2 and 9identified in a real analysis example from a semiconductor productionfacility. The first component vector PC1 is recognizable as a “bow”fingerprint, which an expert may recognize as potentially related todistortions induced by an epitaxy process step. The second componentvector PC2 is a “swirl” component of the type mentioned already andcharacteristic of an annealing step. The ninth component vector PC9 is a“machine” fingerprint characteristic SUSD effects in the litho tool.These fingerprints can be displayed by the PCA apparatus as an aid indiagnosis. As shown in FIG. 11B, other displays/reports can be producedwhich plot 2-D projections of the object data onto selected pairs ofaxes corresponding to respective ones of the component vectors. Thus forexample the top left plot 1002 shows the distribution of wafers by theircoefficient for PC1 against coefficient PC2 (labeled “1 vs 2”). Otherplots 1004 present plots 1 vs 3, 1 vs 4 and so forth as labeled. Thesemay be displayed by the apparatus sequentially or in parallel. In eachplot, the origin of the distribution is not necessarily at the center.Crossed axes 1008 have been added to show the origin.

The pairs of values plotted may be selected by a user, and/or may beselected automatically by the apparatus based on observed correlationbetween component vectors, for example. Labels may be assigned accordingto recognition of reference fingerprints in the library data stored at268. The pairs of values plotted may be guided by hints in the librarydata. For example “when reference fingerprint A is recognized, look forcorrelation with reference fingerprint B”. Note that, after themultivariate analysis is done, the vectors can be projected onto anyvector, not only the identified component vectors.

Not shown in this drawing, but important in a practical embodiment, isthat the samples are plotted again with identifying information, forexample by colors and/or symbols, so that different lots or otherdifferent wafers of interest can be distinguished in their variousclusters, and/or outlier positions. Wafers that are outliers in one plotcan be flagged by color or symbols, so as to reveal their distributionin another plot. In this way, correlations between the differentcomponent vectors can be seen.

At bottom right in FIG. 11B a curve 1012 is displayed plots thepercentage contribution of the distribution that is represented in thevarious component vectors. As the decaying curve 1012 shows, most of theinformation characterizing the distribution is concentrated in the firstfew component vectors, while the contribution due to each furthercomponent vector is ever decreasing. Note that all the informationobtained and displayed can be is obtained from the measured object data,and no reliance need be made on context data (other than the identity ofthe wafers represented). At the same time, the use of contextinformation, such as chuck and/or layer ID may be used, if available.Moreover, the component vectors that are selected as significant emergefrom the data through the analysis, rather than being predeterminedfingerprints (swirl, bow, sombrero etc.) that have been entered ascomponent vectors to be looked for. Therefore investigations will not be“blinkered” by limiting the search to expected effects and sources.Furthermore, the analysis can reveal fingerprints that in themeasurements themselves would otherwise be hidden by much largercontributions. These component vectors may not contribute so much to thepositional deviations of individual alignment marks, but they may be ofsuch a nature that they are not corrected in the alignment model, andconsequently contribute disproportionately to a product performanceparameter such as overlay or CD. Referring to the example of FIG. 11,for example, the SUSD fingerprint represented by component vector PC9may be revealed only because the multivariate analysis effectivelysubtracts the emergent component vectors one by one to reveal eachnext-most-significant component vector in turn.

While the PCA analysis results can be used as an input to automated orsemi-automated root cause analysis, as described below, the results canbe used in various ways without attributing causes to them. For example,having established the distribution of a population of product units inthe low-dimensional spaces represented by for example the 2-D plots inFIG. 11B, an automatic mechanism can be applied to compare object datafrom new product units with the known distributions, to identifyoutliers as soon as they are produced. This will be referred to as“excursion detection”. A lot can be identified as an outlier lot, if itcontains wafers outside the statistical thresholds. Lot-to-lotcorrectable error may be identified as a result. Also lots can sometimesshare certain processing history which makes it easier to trace back theorigin of the outliers. But the analysis can also be done per wafer, andthen the lot behavior can be checked by giving wafers from the same lotthe same symbol. Many aids such as use of different colors and symbolscan be used in a practical apparatus, that cannot be represented in theblack-and-white patent drawings at the scale seen here. Also asindicated, plots can be highlighted (either manually or automatically)as being significant for interpretation. The plots 1 vs 2, 2 vs 3 and 1vs 9 are highlighted in the illustrated example.

As mentioned, the known PCA technique is not the only one that may beused to decompose the multidimensional distribution into a fewsignificant, or “interesting” component vectors. For example, instead ofseeking each first vector that best describes the distribution, onecould program the apparatus to seek a vector such that the distributionof points when projected onto an axis defined by the vector is maximallynon-Gaussian (ICA). Such an approach can be expected more strongly toseparate different clusters, and to highlight for subsequent analysiscontributions that are systematic to one or more parts of the industrialprocess, rather than merely than variations of noise. A projection thatmaximizes class/cluster separability can be the objective of thedecomposition, for example by performing a Fisher mapping. A Fishermapping is a “supervised” multivariate analysis, using some of thecontext data stored at 264 (dotted arrow in FIG. 2). Such context datamight be for example chuck identification (the analysis then beingperformed to maximize information on the influence of chuck-to-chuckvariations), or data identifying an individual etching apparatus. PCAand ICA can be performed as “unsupervised” methods meaning that they donot require context data.

FIG. 12 summarizes in flowchart form the operations performed by PCAapparatus 250, as described above, and RCA apparatus 252, to bedescribed in more detail further below. In a step S1, object data for apopulation of product units (in the example, semiconductor productwafers) is obtained and compiled in a covariance matrix at step S2. AtS3 the covariance matrix is processed by multivariate analysis. Asdescribed already above, the effect of the multivariate analysis is todecompose the distribution of all the vectors in the object data into aset of component vectors, for example component vectors. In step S4 theset of component vectors is processed together with identification ofthe different product units, to analyze the distribution in desiredways. Results may be processed and selected for display partly byautomatic operation and partly by human operator interaction.

The results of the analysis are used in step S5 to provide automaticexcursion detection as production continues. New object data from eachproduct unit or batch (lot) of product units is received at S6 andcompared with the distribution in one more of the component vectordimensions to detect product units lying outside the main distribution(outliers). As seen in FIG. 10, this comparison can be in one or moredimensions. Optionally, the new object data can be added to thecovariance matrix and used to update the decomposition into componentvectors. Upon detection of outliers (excursions), the manufacturingprocess can be interrupted in a serious case, or an alarm can be raised.Further measurement may be triggered, for example to decide whethercertain product units or lot of product units can proceed to a nextprocess step, or needs reworking, or needs to be discarded.Alternatively, these outcomes can be triggered directly on the basis ofthe component vector analysis.

Second Diagnostic Apparatus

At step S7 in FIG. 12, root cause analysis is performed in RCA apparatus252. This apparatus combines the results of the decomposition intocomponent vectors with performance data obtained in step S8 and/orcontext data obtained in step S9. The results of the root cause analysismay be displayed or reported at step S10, or they may be used togenerate corrections to process control settings at step S11. At stepS12, production continues for new product units (for examplesemiconductor product wafers), applying the corrections to improve theproduced products by reducing one or more of the identifiedfingerprints.

Not all identified fingerprints can or should be corrected. Defining afingerprint correction may be regarded as a permanent solution to theissues revealed by the analysis, or it may be that servicing orreplacement of a responsible apparatus is required. Correction may beuseful as a temporary measure until the responsible processing apparatuscan be recalibrated or repaired. If the error is not correctablesufficiently, the apparatus in question may be omitted from processing(or reassigned to less critical operations). In addition, it should benoted that to correct some fingerprints might make a performanceparameter such as overlay worse, not better. This is because afingerprint that remains consistent from layer to layer introduces nooverlay error at all, whereas to identify such a fingerprint and attemptto correct it in subsequent layers would introduce overlay.Identification of fingerprints that should not be corrected can bestored and exploited by removing this component vector when calculatingthe corrections for each product unit.

Furthermore, fingerprints that should be corrected may be present onlyin some of the product units. Where PCA apparatus 250 and/or RCAapparatus 252 has been used to identify the context in which certainfingerprints arise, corrections may be generated with associated contextcriteria, so that they may be applied selectively in the processing offurther product units, depending on the processing history of thoseparticular product units. Thus, corrections may be applied to a productunit only when the processing history of that unit matches the contextcriteria associated with that correction. It will be understood that, ina lithographic process, corrections will often be selected and appliedon a batch or lot basis, rather than for each individual wafer.Furthermore, it will be understood that corrections may be applied inthe lithographic operation, that are designed to correct fingerprintsarising from the physical and/or chemical operations to which productunits have been subjected. Context criteria can be defined in terms ofthe information extracted from the results of the multivariate analysis,rather than explicit context data.

Without needing to know in advance what parameters will be of interest,collection of alignment data and or other object data can be performedin the background of the normal manufacturing process. If possible,process context data and other identifying data can be gathered. Some ofthis data can be collected in an anonymized form, so thatconfidentiality of a process can be respected, while outsourcing theanalysis. Within the overall form of the embodiment described, a number“use cases” can be envisaged for the new apparatus. Example functionsfor a commercial embodiment include: a “one button push” to showfingerprints (the top 10, say) plus mean fingerprint (“PC0”); automaticsuggestion of labels for component vectors or clusters of componentvectors (e.g. using data scatter); automatic estimation of theperformance impact (for example in nanometers of overlay) of aparticular component vector or group of component vectors. A qualitativeassessment of overlay impact of a certain alignment component vector canbe made from alignment-overlay (performance data) correlation analysis,even if detailed simulations sufficient for a quantitative calculationare not undertaken.

The user interface can provide for an operator to ask for ‘relevantfingerprints’ and will report a short list of: Outlier wafers and lots;Processing tools co-occurring with outliers. The user interface 1200 andvisualizer 1202 can visualize alignment deltas of various types (seebelow with reference to FIGS. 16 and 17); (color-to-color, step-to-step(layer-to-layer)). It can visualize scatter of the dataset, allow forautomatic clustering and visualization of a “mean wafer” (average wafer)per cluster. The co-occurrence of tools and fingerprints can beexploited automatically for example by a Bayesian network or by derivingsets of co-occurrence patterns representing frequently occurringprocessing tool sets. If performance data such as overlay is alsoavailable, the apparatus can correlate this with the component vectorsobserved in the object data (FIG. 15 below).

In another category of uses, instead of the step S11 of generatingcorrections as normally understood, the apparatus can generate otherdata (recipes) for controlling or advising on some aspect of subsequentprocessing. In a particular example, an “Alignment advisor” can be made,which suggests better operation of the alignment sensors themselves.(see discussion of FIG. 17 below.) A “library” of fingerprints can beaccumulated in the storage 268, by which recipes suitable for aparticular situation can be retrieved upon observation of fingerprintssimilar to those observed before.

Further variations and applications include: analysis of overlay asobject data, color-to-color analysis of alignment data; observation ofintrafield fingerprints rather than (only) the interfield fingerprintsillustrated herein; improved “flyer removal”.

With regard to color-to-color analysis, for example, it may be notedthat alignment sensors AS will typically illuminate the alignmenttargets with a range of different wavelengths of radiation (colors), toimprove the chance of a good position reading through overlying layers.Often an alignment “recipe” will simply select a single the “best” colorto use to read marks in a given situation, and other data is discarded.Comparison between signals obtained with different colors can howeverreveal interesting diagnostic information. In particular, color-to-colordifferences can indicate the presence of mark asymmetry, wherestructures within a mark have become distorted by processing.Corrections for subsequent processing steps can then generateddifferently, depending whether it is judged that a fingerprintrepresented apparent deviations caused by mark deformation and themeasurement process, rather than actual positional deviations of themarks.

Flyer removal refers to the identification of individual marks that areoutliers relative to the other marks on the same wafer. The occurrenceof such “flyers” can be due to a variety of local factors, which can beeasier to recognize using the identified component vectors.

Root Cause Analysis Examples

Expanding now on RCA apparatus 252 and step S5 in the flowchart of FIG.12, various techniques are available to the operator of the system, forperforming analysis to identify the root cause of the fingerprints(component vectors) present in the analyzed product units. Referringback to FIG. 5, it will be recalled that certain fingerprints arerecognizably associated with certain processing steps. Thus, if a“swirl” fingerprint PC1 emerges as a contributor in a number of thewafers (and not in others), annealing processes and apparatuses becomesuspect as causes of the fingerprint. This is the situation illustratedin FIG. 13. Similarly, if a “scaling” fingerprint PC2 is observed to bestrong in a number of the wafers, it may be suspected that positionaldeviations are partly the result of physical distortions introduced byan etch step. In each case, as illustrated, statistical calculationsbased for example on Gaussian distributions and sigma (standarddeviation) values can be employed to distinguish “outlier” wafers 1100having a lot of swirl from “normal” wafers 1102, and to distinguishoutlier wafers 1110 having a strong scaling fingerprint from normalwafers 1112. Note that, although some wafers have a strong positivecoefficient and others have a strong negative coefficient, these areboth indicative of a strongly expressed fingerprint, only with adifferent sign. The apparatus in this example will group both positiveand negative outliers together as equals. The apparatus can offer afunction to group positive and negative outliers separately, if desired.

If the product units in question have reached such a stage in theirhistory that they have undergone several annealing steps and otherprocessing steps, potentially in different apparatuses, the reason whysome of them have stronger fingerprints than others may be hard todetermine without automated assistance.

As shown in FIG. 12, RCA apparatus 252 in one embodiment uses thedetermined component vectors (fingerprints) in combination with contextdata from storage 264 to identify correlations between the strength ofthe identified fingerprints and certain events, apparatuses, orparameters in the history of the product units represented in the objectdata. Analysis is performed to identify correlations between (i) thecontext data 264 representing history of the product units and (ii) thepositions of those product units in the multidimensional spacerepresented by the component vectors that have emerged from multivariateanalysis of the object data 260. There are many forms this analysis maytake, so that RCA apparatus in practice can offer a suite of functions,to be used according to the task at hand. In addition to context data,performance data 266 can be used to find correlations between certainperformance parameters (CD, overlay) measured from the product units andthe component vectors identified in the multivariate analysis.

In the illustrated example, a network 1120 of co-occurrence relations isestablished between the occurrence of certain processing apparatus(tools) TL#1, TL#2 and TL#3 in the history of a wafer and thefingerprints PC1 and PC2 in the object data. These three apparatuses maybe nominally identical and should perform identically, but theinvestigation will reveal if one or more of them are causing unwantedeffects in practice. In principle, the analysis can be performed“blindly” to seek correlation between any of the identified fingerprintsand any or all of the events and apparatuses in the histories of theproduct units, and for all parameters of the context data.Alternatively, as in the illustrated example, some human or machineexpertise can be applied to identify that the observed fingerprints arecharacteristic of etch and anneal steps, and to seek correlationsbetween the occurrence of the fingerprints and the use of certain toolsor tool clusters that may have been used perform those particular steps.In the illustrated example, the analysis reports co-occurrence analysisvalues representing the percentage of wafers having each tool in theirhistory, that display the fingerprint strongly. This report reveals thatamong the three tools, 40% (fraction 0.4) of the wafers that have atsome point in their history been processed using tool TL#1 have a strongfingerprint PC1 (large coefficient c(PC1)), while the correspondingpercentages for tools Tl#2 and TL#3 are only 5%.

Thus, tool TL#1 is strongly implicated as a cause of poor performance inthe production process. This can trigger further investigation and/orrecalibration of the implicated tool. It may also trigger the generationof a history-dependent correction (FIG. 12 step S11). This correction isan addition to the alignment model, that can be applied automatically insubsequent lithographic patterning steps, whenever context dataindicates the use of that particular tool or tools in the history of thewafers being processed. Noting that several tools are associated withthe same fingerprint PCX, it will also be appreciated that thefingerprint actually added to each wafer by the implicated tools maydiffer slightly from one another. The fingerprint PCX is however usefulas an approximation to those individual fingerprints. Searching throughthe other component vectors may reveal minor fingerprints and hence morespecific corrections that can be assigned to each specific tool, if suchaccuracy is deemed necessary. In either case, each correction is storedin association with context criteria so that context data for wafers insubsequent steps can be used to determine whether that correction shouldbe applied. Processing of subsequent wafers can therefore be improved,irrespective of whether those wafers have been included in the analysis.

On the other hand, in relation to wafers that are outliers in thedistribution of component vector PC2, tool TL#1 is only weaklyimplicated (co-occurrence analysis value 10%), while tools TL#2 and TL#3both have higher co-occurrence analysis values (20%, 20%). It will beunderstood that these results are not conclusive of a fault in a certaintool. Further investigation will generally be required, for example toidentify what other factors in the context data can explain why 20% ofthe wafers processed by tool TL#2 have a strong fingerprint PC2, but 80%do not. However, the automation provided by RCA apparatus using theresults of the multivariate analysis is useful in at least focusingattention on the right part of the process. The findings may trigger acorrection to be generated, either automatically or with userinteraction, as described above with reference to step S11 in FIG. 12.

In the illustrated example, the context data of interest is categoricalin nature, and signifies whether a certain processing apparatus (etcher,deposition chamber etc.) or set of tools was involved in the history ofprocessing each wafer. By “categorical” we mean that a given feature orevent was either present (one or more times) in the history of a productunit, or was not. Other context data, such as a parameter indicatingwhat temperature setting was used in a particular process step or whatstrength of correction was applied in a process correction in the lithotool, can be continuous in nature. When it comes to performance data266, this also can be categorical or continuous in nature. Continuousdata can be turned into categorical data if desired. For example,overlay data may be continuous in nature, but wafers can be categorizedfor example according to which wafers are outliers in the distributionof overlay values, which wafers are not outliers in the distribution ofoverlay values, or which wafers fall outside some absolute performancespecification. The component vectors PC1 etc. can also be treated ascontinuous variables, or they may be categorized, as in the illustratedexample.

Where the context data or performance data it is categorical,co-occurrence relations can be sought in the manner described above bydiscovering frequently co-occurring sets of categorical items (i.e.tools and outliers). One particular implementation of the co-occurrencerelation discovery concerns a particular pre-processing of the availabledata and a particular type of co-occurrence pattern to be found.

In this scenario, a single database

is constructed that joins both object data and context data (and/orperformance data) for each product unit. Given that the projection ofthe object data of each product unit is continuous, it is firstdiscretized in order for it to be useful for discovering the consideredco-occurrence patterns.

A possible method to discretize the projections is to determine whethereach product unit constitutes an outlier with respect to one or morefingerprints, given the distribution of the projections of all productunits. This leads to a binary version of the projected object data,stating whether or not this product unit is an outlier given theunderlying distributions.

Each row in the resulting database consists of the product units'outlier indications of the object data projections and the context data(and/or performance data). A co-occurring pattern c can be defined as asubset of the possible variables in

, and their particular instantiations (e.g. PCA_1=outlier, andTool_1=Etcher_A).

Each pattern c can be considered as a local model that describes aspecific part of

. By selecting a set of patterns c, denoted by

, a model for the complete database can be constructed. The choice ofmodel

depends on a chosen optimization criterion. One instantiation of thiscriterion is to consider an encoding scheme that assigns each encoder

a particular encoded database length. In this setting, the best encoderis the optimal model.

An optimal co-occurrence pattern set

contains significant (given the chosen optimization criterion) relationsbetween variables in

(discretized object data, context data, and/or performance data). Thisset

can be used to make the relation between tools and component vectorsapparent.

A probabilistic analysis, for example using a Bayesian network, can beused whether the context data is either categorical or continuous ordiscrete. In this approach, a network is constructed which representsvia ‘network parameters’ θ the joint probability that a component vectoroutlier occurs when a certain processing tool is used. An initial choicefor the joint probabilities may be specified by a skilled engineer, orby studying tool-fingerprint occurrences from historic datasets. Thisinitialization specifies a ‘prior probability’ on tool-fingerprintco-occurrence as a ‘prior’ on the network parameters P(

). In a Bayesian network, observations on occurrence of fingerprintsand/or involvement of processing tools from new product units can beentered as ‘evidence’ (data) D in the network. The likelihood p(D|θ) ofthe observations given the current network parameters is computed andcombined with the prior p(θ) into a posterior probability p(θ|D) on thenetwork parameters given the data. This can be done using Bayes' rule ofinference:

${p( {\theta D} )} = \frac{{p( {D\theta} )} \cdot {p(\theta)}}{p(D)}$

Postulation of conditional independencies between variables (occurrenceof certain tools and fingerprints) may be used to make computation ofposterior parameter probabilities (‘Bayesian inference’) tractable, orone may rely on computing the parameter setting θ* that maximizes the aposteriori probability,

θ*_(MAP)=argmax_(θ) P(θ|D).

In the case where a flat prior is assumed (i.e. without prior knowledgeon the probability of joint tool-fingerprint occurrence), this lastexpression reduces to the maximum likelihood estimate:

θ*_(ML)=argmax_(θ) P(D|θ).

By this mechanism, spatial measurement data and/or context data fromnewly incoming product units can be used to update the probability ofco-occurrence for the particular use case and fully customize whensufficient data arrives. Note that observation of either spatialmeasurement data or context data (or both) for new product units isallowed, since probabilities on any of the missing (non-observed)variables may be inferred via aforementioned Bayes' rule of inference.

The results of the probabilistic analysis can be used to make inferencesabout causes and effects. The type and complexity of the analysis is amatter of design choice. The methods described above are only examples.From experimental use of the present apparatus, for example, instanceshave been observed where the presence of a fingerprint of interest iscorrelated most strongly not with the occurrence of any one apparatus orprocessing operation alone, but with the occurrence of a particularsequence of operations or apparatuses. The RCA apparatus can thereforeprovide functions for identifying such sequences as a parameter in thecontext data.

FIG. 14 shows schematically another mode of operation of RCA apparatus252, in which graphic visualization is used to allow correlations to beobserved by a human operator. At the top of the diagram, it is shown howthe PCA apparatus 250 and RCA apparatus 252 share common user interface1200 and visualization module 1202, which may be implemented byconventional computer input devices and display screens. At the bottomof FIG. 14 is shown an example of a display 1204 produced byvisualization module 1202. This display provides a particular projectionof the object data decomposed into component vectors PC1, PC2 etc.,plotted together with the context data representing (in this example)the involvement of certain tools in the processing history.

At 1210 there is illustrated a “swirl” component vector PCX that hasbeen identified as being of interest among the component vectors PC1etc. identified by PCA apparatus 250. At 1212 there is shown an extractfrom a process sequence that may be represented in the context data as avector P(wafer). Each element in the vector represents a step in thehistory of the wafer, including not only the type of step performed butalso the individual tool or tool cluster used to perform that step. Thecontext data for example illustrates whether a tool TL#Y was used. Thelevel of detail provided in the context data is arbitrary and willdepend on what can be obtained in a given situation. The use of theobject data in the multivariate analysis allows the fingerprints to beidentified independently of any context data, and then used incombination with such context data as is available.

The display 1204 is a representation of wafers plotted at points in athree dimensional space defined by the occurrence of three particulartools in the processing history, these being tools TL#1, TL#3 and TL#4.This may be for example a next step in a root cause analysis procedure,following the identification of these particular tools as suspectsthrough the co-occurrence analysis illustrated in FIG. 13. Tools mayalternatively be identified as suspects by deriving sets ofco-occurrence patterns representing frequently occurring processing toolsets. In the processing of wafers, each wafer may visit a tool more thanonce, and the wafers are plotted in the three-dimensional spaceaccording to how many times they have visited a given tool (0, 1, 2, 3times etc.). Wafers having a strong fingerprint (large coefficientc(PCX)) are highlighted by solid dots in the plot, while wafers nothaving this fingerprint are white (open) dots.

This plot reveals a great deal about the influence of each tool on thefingerprint PCX. The wafers that have no involvement of any of thesuspect tools TL#1, TL#3,TL#4 are plotted at 1220. As can be seen, theseare all represented by white dots and do not have the strong fingerprintPCX. On the TL#1 axis, one can see a few wafers having a strongfingerprint if they have been processed two or more times by tool TL#1(1222). On the TL#3 axis, we see that any wafer that has been processedonce or twice by tool TL#3 is showing a strong fingerprint PCX (1224).On the TL#4 axis (vertical direction as plotted), some wafers have beenprocessed once by tool TL#4 (with or without also being processed by theother tools) and these all have the fingerprint PCX (1226). From thisvisualization, the RCA apparatus reveals that tool TL#1, though used inthe processing of some wafers that show the strong fingerprint, is notthe cause of that fingerprint in most cases. Rather the tools TL#3 andTL#4 are more likely to be the cause. At the same time, the fingerprintdoes seem to be introduced by repeated use of the tool TL#1, as well.

While in the example just described, graphic visualization is used toallow correlations to be observed by a human operator, the actions ofthe human operator in spotting patterns of correlations and clusteringcan be automated if desired.

The findings may trigger a correction to be generated, eitherautomatically or with user interaction, as described above withreference to step S11 in FIG. 12 and FIG. 13.

FIG. 15 illustrates another mode of operation of RCA apparatus 252, thistime correlating performance data 264 with the results of themultivariate analysis performed on the object data by PCA apparatus 250.The same user interface 1200 and visualization module 1202 can beemployed. The performance data in the illustrated example is overlaydata measured on the wafers after certain processing steps. Themeasurements can be taken for example using the metrology apparatus 240of FIG. 2.

It will be seen that in this case the performance data iscontinuous-valued, rather than categorical data. Display 1240 presentsgraphs 1242, 1244 plotting wafers (all represented by solid dots)against axes of overlay (OVL) (vertical axis) and strength offingerprint PC1 (horizontal axis, graph 1242) and fingerprint PC2(horizontal axis, graph 1244). In graph 1242 it can be seen byinspection that there is a strong correlation between the performance interms of overlay and the strength of the fingerprint PC1, while graph1244 shows no correlation. This allows the operator immediately toidentify which of the component vectors is associated with observedperformance problems. In particular, it may be that an apparently strongfingerprint has no bad influence on performance, while a relativelyweaker fingerprint has a strongly adverse influence. This can be forexample because the stronger fingerprint is reliably corrected in thealignment model (FIG. 6), or contributes equally in each layer thereforehaving no influence on overlay. With the RCA apparatus providing thisinsight, root cause analysis becomes a very much easier process.

The findings may trigger a correction to be generated, eitherautomatically or with user interaction, as described above withreference to step S11 in FIG. 12 and FIG. 13.

Aside from the visualization for interpretation by a human operator, astatistical analysis such as linear regression (line-fitting) can beperformed to quantify the degree of correlation (correlationcoefficient) between performance data ad component vectors(fingerprints). The result of this analysis is illustrated on graph 1242by a best-fit line 1246. Since correlation can be quantified in thisway, the identification of implicated fingerprints can be automated. Thevisualization as such is therefore an optional part of the root causeanalysis. Note that overlay, CD and other “performance” parameters, ifmeasured consistently at points spatially distributed across each wafer,can also be used as object data, if desired.

FIG. 16 shows another mode of operation of the RCA apparatus foridentifying layer-to-layer variations in the processing of individualwafers. As mentioned above, the object data may include multipleinstances of the same product unit, where it has been measured atdifferent stages in processing. The context data 264 includesinformation connecting these instances, so that the development of thefingerprints in the same product unit can be plotted as a function ofits progress through the process. Note that the layer-to-layerrelationships could also be in practice contained already as part of theidentifying label of each entry in the object data. It is the use of thedata in the root cause analysis that makes it considered as context datafor the purposes of the present disclosure.

In FIG. 16, visualization module 1202 provides a display 1260 in whichwafers are plotted against two of the identified component vectors PC1and PC2. These two component vectors may have been identified as beingof particular interest by a previous step, for example the co-occurrenceanalysis shown in FIG. 13, or by correlation with performance data asshown in FIG. 15. Alternatively, RCA apparatus may display or analyzemany combinations of parameters in turn. It will be recognized thatdisplay 1260 shows the same plot as seen in FIG. 10C. As explained inrelation to FIG. 10C, the plot and the applied threshold 930 reveal twowafers to be outliers, represented by plotted points 906. Display 1260allows the history of development of the fingerprints in thecorresponding wafers to be revealed. Suppose it is observed that point906 represents a wafer W(i) at a stage in the process where a layernumber 5 is being processed. This can be labeled W(i,L5). The userinterface 1200 allows an operator to ask for previous instances of thesame wafer to be highlighted in the display. As seen, this highlightingreveals the previous instances W(i,L4) and W(i,L3) among the manyhundreds of points plotted. Furthermore, once they have beenhighlighted, it is obvious to the operator that the fingerprint has beenintroduced specifically in some processing step after the measurement ofthe wafer at layer 4 and before measurement at layer 5, that is to say,somewhere in the step 1304. This greatly aids identification of the rootcause of the fingerprint. Where the tools used for each layer are thesame, it may be found for example that a particular combination orsequence of steps is the cause of distortion being introduced in thestep

While simple inspection of the display of FIG. 16 reveals very clearlythe step change in fingerprints between instances W(i,L4) and W(i,L5),this assumes that the relevant pair of component vectors have beenidentified. The RCA apparatus 252 in this embodiment includes anautomated tool to “mine” the data and reveal the relevant componentvectors is desirable. The change in fingerprint coefficients betweeninstances can be referred to as “deltas” (labeled A for illustration inFIG. 16). Deltas can be one-dimensional, with the number of deltas beingoptionally up to the number of component vectors identified in themultivariate analysis, or they can be multidimensional if required. Forexample, looking at the two-dimensional plot of FIG. 16, it may besufficient to identify the step in the strength of component vector PC1,or it may be preferred to identify as delta a (Euclidean) distance inthe two-dimensional space defined by the selected component vectors.

By calculating the deltas at each stage in the process, for allcomponent vectors if desired, large step changes (such as the oneillustrated in FIG. 16) can be identified automatically and reported.This can be a trigger for use of the other modes of analysis,illustrated in FIGS. 13 to 15, and/or investigation on the tool itself.Especially where a component vector just changes gradually with eachimplicated process step, it may be that the issue is solved by acorrection generated, either automatically or with user interaction, asdescribed above with reference to step S11 in FIG. 12 and FIG. 13.

The interaction between deltas and the multivariate analysis can takemany forms. Deltas between the coefficients of the identified componentvectors can be calculated and analyzed, as just described. Alternativelyor in addition, deltas can be calculated between the measurement data,and then those deltas subjected to multivariate analysis. As a furtheralternative, deltas can be calculated between the measurement data forproduct units of interest, and then analyzed in terms of the componentvectors identified from the analysis of the object data for thepopulation as a whole. In summary, the diagnostic method may includeobserving changes between the measurements of a product unit atdifferent stages in the industrial process for one or more same productunits, and projecting the measured variation onto one or more of thecomponent vectors identified in the multivariate analysis. This can beuseful for verifying the results of the analysis illustrated in FIG. 16.An example will be described with reference to FIG. 17.

In FIG. 17, different process steps between layers L1, L2 etc. arelabeled 1300-1306. The object data AL for a given wafer revealsfingerprint PC1 (for example) which gets stronger from the start (AL0)to the finish of the process (AL4). Suppose the analysis illustrated inFIG. 16 suggests that component vectors PC2 and especially PC1 areshowing a step change in step 1304. This result can be verified bycalculating and displaying deltas between the alignment measurements (orother object data) as seen at the bottom of FIG. 17. It can be seenimmediately that ΔAL(1,2) representing the change caused by process step1302 is virtually zero, while ΔAL(2,3) representing the change caused byprocess step 1304 has a dominant dual-swirl fingerprint. If this dualswirl fingerprint is the one represented by component vector PC1, thenthe display tends to confirm that the physical data corresponds to theresults of the mathematical analysis performed by the apparatus.

It will be understood that there are many ways the that the types ofanalysis disclosed herein can be applied to perform a robust root causeanalysis. In another scenario, the delta identified by analysis in FIG.16 might not be the dominant fingerprint in the deltas betweenmeasurements. In that case, it could be that there is a flaw in theanalysis, or it could be that the fingerprint component vector PC1highlighted in FIG. 16 is a minor one (in the context of the step 1304),and is masked by the dual swirl fingerprint seen at AL(2,3) in thedrawing. The set of component vectors can be used as a “probe” to revealhidden component vectors in the deltas ΔAL(1,2) and ΔAL(2,3) byprojecting them onto the component vectors already identified.

While the analysis just described refers to a single wafer (productunit), more robust analysis will be performed in practice, based onstatistically significant populations of product units. For example, thebehavior of RCA apparatus 252 can be made different in practice if thelarge delta observed in FIG. 17 occurs in only one wafer of a lot,compared with when it is observed in all wafers undergoing the sameprocess step 1304. If it is found that the large delta occurs in somewafers (or some lots) but not others, this analysis can be combined withthe modes shown in FIGS. 13 and 14 to correlate the observance of thedelta with the involvement of specific tools in the process. The processis the same as illustrated in FIG. 13 or 14, with the delta infingerprint strength being used in placed of the fingerprint strengthitself.

The above example refers to deltas between different instances of thesame product unit measured at different stages in an industrial process,that may be referred to as “step-to-step” or “layer-to-layer” deltas,other types of delta may be made, if the object data is available. As aparticular example, the object data may include different measurementsof the same property, made by different sensors, or the same sensoroperating with different parameters. For example, the alignment sensorin a commercial lithographic tool generally provides a number ofdifferent operating modes using different colors (wavelengths) ofradiation, different polarization, illumination profile and so forth.This is to recognize that different product types, and different layerswithin the product, contain a wide range of materials and types ofmarks. In addition to controlling these parameters, an “alignmentrecipe” will generally specify what subset of the alignment marks are tobe measured across the wafer, to save time and improve throughput. Nosingle “recipe” is suitable for measuring every layer on every product.The new apparatus can reveal opportunities for selecting a betterrecipe, based on observation of the selected recipe in practice, and/orby recognizing certain types of fingerprints that in turn suggest aparticular recipe will be favored.

As a simple example of the latter feature, where a “scaling” fingerprinthas been identified, the alignment recipe for future steps may beadjusted to include more marks in a peripheral region of the wafer. Asanother example, it may be that a certain identified fingerprint isknown to be indicative of mark deformation, which in turn means thatpositions reported for these marks will be subject to inaccuracy.Different marks or a different mode of measurement of the marks may beselected that will be less prone to this deformation, so as to improvethe accuracy of the positional measurements. Rather than selecting ordeselecting a mark completely for the alignment, marks may have theirweighting increased or decreased in the calculation of the alignmentmodel.

More generally, then, the novel apparatus can provide a range of“alignment advisor” functions. The apparatus can simulate the residualsthat would occur when different alignment models were to be chosen andevaluate their appropriateness by projecting these simulated residualson the component vectors determined from the initial object data. Usingperformance data such as overlay data, the apparatus can help identifycorrelation between high-overlay product units and the component vectorscores according to the corresponding alignment object data. Hence,observing similar scores in new product units may be indicative ofperformance degradation and may be used for timely corrective actions.In addition, object data measurement locations could be optimized inorder to better capture the pattern according to certain componentvectors (e.g. wafer deformation patterns) and/or suppress the patterndue to other component vectors (e.g. mark deformation patterns).Furthermore, attributing certain component vectors to their origins(e.g. processing tool etch chamber, anneal chamber or perhaps litho toolstep-and-scan operation) can be aided by relating the vectors to certainvector patterns known upfront to occur with certain processing functionsand may lead to dedicated options (corrective; diagnostic) for furtherprocess optimization.

Any or all of these functions can be linked to the fingerprint librarystored at 268. Fingerprints found in new wafers can be mapped to thosein the library, to retrieve interpretations and recommended recipechanges.

Alternative Implementations

As mentioned already above, alternative implementations are possiblewithout deviating from the principles of the present disclosure. Recallthat, in the implementation described above and illustrated in FIGS. 7to 9, the object data is arranged into vectors to form a covariancematrix for the purposes of PCA in such a way that each vector ALrepresents measurements of one product unit (e.g. wafer). The elementsof that vector are x, y deviations measured from alignment marks atpoints spatially distributed across the product unit. Consequently, thedifferent dimensions of the multidimensional space are the values of theparameter of interest measured at the different positions on the wafer.The number of dimensions corresponds to the number of measureddeviations per wafer, and we can refer to this multidimensional space as“mark space”, by reference to the marks from which these deviations aremeasured. Note that, in those implementations, both the object dataobtained by measurements and the component vectors obtained by themultivariate analysis are expressed in the same multidimensional space.As will now be explained, alternative implementations are possible, sothat the object data prior to and during the multivariate analysis isnot necessarily expressed in the same multidimensional space as thecomponent vectors that are ultimately obtained.

FIG. 18 illustrates for example a first alternative implementation whichexpresses the object data as vectors in a multidimensional space, but itis a different multidimensional space rom that in which the resultingcomponent vectors will be expressed. In each vector represents theparameter of interest measured at one spatial location, over a number ofdifferent product units (e.g. wafers). In this alternativeimplementation, each vector would correspond to one of the measurementpoints, and each element of the vector represents the measured value ofthat parameter at that point on a different respective one of theproduct units. Consequently, the different dimensions of themultidimensional space would be the values of the parameter measured atthe that location on the different wafers.

In the example where the parameter of interest is x and y positionaldeviations measured from alignment marks, then the roles of wafers andmarks are interchanged compared with the implementations illustrated inFIGS. 7 to 9. The set of spatial wafer measurements are represented asmultiple spatial observations defining 2n vectors X(j) in a spacespanned by the set of m wafers. The correspondence between themeasurements from a set of wafers and the elements of the vectors isillustrated graphically in FIG. 18. The multidimensional space in whichthe object data are expressed may be referred to as “wafer space”, incontrast to the “mark space” used in the previous examples.Mathematically, this means that a (wafer) covariance matrix Σ_(W) can beexpressed as:

Σ_(W) =E[X(1−2n)*X(1−2n)^(T)]

where X(1-2n) is a matrix expressing the object data as a set of 2nvectors whose elements are the measurements of x or y deviation on mdifferent wafers. This wafer covariance matrix Σ_(W) has dimension m×mwhere in the earlier implementation the mark covariance matrix Σ hasdimension 2n×2n.

It will be understood that in these different implementations the sameobject data is represented, merely in transposed forms. Indeed anotherrepresentation of the wafer covariance matrix is simply:

Σ_(W) =E[AL(1−m)^(T) *AL(1−m)]

using the same notation as the (mark) covariance matrix in FIG. 8. Inother words PCA other multivariate analysis can be performed using themark covariance matrix Σ or the wafer covariance matrix Σ_(W). Moreover,it can be shown that, provided the means of the columns and the means ofthe rows in the object data matrix (AL(1-m) or X(1-2n)) are also zero,the results of the analysis, when expressed as component vectors in themark space, will be the same. This condition applies in embodimentswhere the mean vector is subtracted, as illustrated for example in FIG.9B.

More specifically, consider that the wafer covariance matrix Σ_(W) ofdimension m×m is diagonalized in the course of the PCA analysisprocedure. When both the mean of the columns and the mean of the rows issubtracted, the normalized component vectors (eigenvectors) and henceany projections of the data onto this basis, are the same as obtainedwith the first implementation (where the mark covariance matrix isdiagonalized). The component vectors obtained by this alternative methodcan thus be used to extract diagnostic information in the same ways asalready described above, and as further described below.

In yet another embodiment of the method, a singular value decomposition(SVD) of the object data is performed as a form of multivariateanalysis. In the SVD method the object data is analyzed directly inmatrix form, and not explicitly expressed as vectors in anymultidimensional space. However, with straightforward manipulations ofthe results one can again obtain component vectors expressed in amultidimensional space where they can be used to extract diagnosticinformation as already described above, and as further described below.

We further remark that subtraction of the mean wafer as practiced in ourexemplary embodiments is not strictly necessary for a component vectordecomposition of spatial measurements on multiple wafers or otherproduct units. When the mean wafer is not subtracted, a dominantcomponent vector may be aligned with the average.

It goes without saying that all of the implementations disclosed hereincan be applied to measurements of any parameter at points spatiallydistributed across any type of product unit. The terms “mark space” and“wafer space” are used purely for illustration, and do not imply thatthe concepts behind them are limited to the example of alignment markson semiconductor wafers.

High Resolution Reconstruction of Low Resolution Data Based onMultivariate Analysis Results

As detailed above, various manufacturing process disturbances associatedwith specific fingerprints may affect the manufacturing process.Clearly, it is desirable during ‘real time’ manufacturing process torapidly detect process disturbances/or corresponding fingerprints and/orto correct or counteract systematic process disturbances. The processmonitoring system mentioned above is for that purpose. It is alsodesirable to reduce the time and metrology resources dedicated tomethods and associated apparatuses for the detection and correction ofprocess disturbances.

Disclosed in this section are a method and associated apparatus forimproving the detection of manufacturing process disturbances, enablingsystematic correction of manufacturing process disturbances usingavailable manufacturing resources (e.g. stored process data). The methodexploits the results of multivariate analysis performed on historicmeasurements, such as for example the PCA analysis in the embodimentdescribed here.

Dense measurements (i.e. with a high spatial resolution) are regularlycarried out in order to monitor process performance and (if necessary)to generate associated corrections for process optimization purposes.However, measurements a with high spatial resolution consume time andresources, so they tend to be made on a few lots only.

Sparse measurements (i.e. with a low spatial resolution) are carried outon each wafer in order to monitor time and sparse spatial measurementvariations. Low resolution measurements/data (referred to below assparse object data) may be collected before exposure, for example atmeasurement station MEA and/or after exposure, with one or moremetrology apparatus 240.

FIG. 19 presents the principle of a performance monitoring function inthe production facility of FIG. 2. The method can be implemented in thecontext of monitoring step S5 in the method of FIG. 12. The method canbe applied using the result of multivariate analysis of measured objectdata, whether or not other steps such as root cause analysis are alsoperformed using the same or different object data. As shown in FIG. 18,measurements are carried out of a desired process performance indicatorPI, to determine whether the manufacturing process drifts outside acontrol limit CL region delimited by an upper limit (UL) and a lowerlimit (LL). The measurements in this context may be regarded asperformance data, but in the present example they relate to the sameparameter as the object data which has been collected and subjected tomultivariate analysis. The horizontal axis represents time or, in thecontext of a mass production process for semiconductor wafers, wafernumber or lot number. As mentioned already, some wafers or lots will bemeasured with a high spatial resolution (referred to hereinafter asdense measurements) while the majority of monitoring measurements willbe performed with a low spatial resolution (sparse measurements), tosave time.

Referring now to FIG. 20, we present the principle of a reconstructionmethod, whereby a multivariate analysis technique such as principalcomponent analysis (PCA) may be applied to enhance the effective spatialresolution of sparse measurements during process performance monitoring.This may be referred to as super-resolution reconstruction of sparsemeasurements by performing history based spatial interpolation forimproving the accuracy of estimated fingerprints for each wafer. It isproposed to reconstruct a given sparse measurement by, for example,linearly combining stored dense component vectors obtained fromhistorical dense measurement data from wafers similar to the presentwafers. Note that the example of super-resolution reconstructionpresented in this section is PCA based. Other forms of multivariateanalysis may also be employed in the reconstruction process.

FIG. 20 presents an example of a PCA based reconstruction method. It isassumed that dense (high spatial resolution) measurements have been madeof a number of past wafers, corresponding to a particular layer andproduct design. In the context of the method of FIG. 12, for example,these measurements are taken in steps S1 and S5. The measurements may befor example a CD measurement, overlay or focus, depending whichparameter is desired to serve as performance indicator PI for theprocess monitoring. PCA apparatus 250 has processed these densemeasurements to obtain a set of component vectors or “fingerprints”.(The measured parameter is therefore considered object data for thepurpose of this analysis, while it has also been used above as anexample of “performance data”, for RCA apparatus 252. In the context ofthe present example, it may also be referred to as “monitoring data”.)These component vectors are stored in a library at 268. The librarypotentially also includes fingerprints obtained by PCA on data fromdifferent layers and different products. Context data (not illustratedin FIG. 20) identifies which elements in the database are relevant towhich layers and products.

Subsequently (for example in the course of monitoring step S5 of FIG.12) at step S20 a newly patterned wafer is subjected to sparsemeasurement of the same parameter (for example CD). The componentvectors PC_(n), calculated from the high resolution measurements by PCAapparatus 250, are retrieved from the library at S21, using context dataidentifying the product and layer to ensure that the relevant componentvectors are retrieved.

At step S22, a subset of the dense component vectors (PC1, PC2 . . .PCN) may be selected from those stored in the library. For example, theselected component vectors may correspond only to those withcoefficients surpassing those of equivalent pure Gaussian randomness.Otherwise, the results of analysis might be influenced undesirable bywhat is only noise. Other selection criteria may be applied, for examplebased on more detailed context data where root cause analysis has beenperformed by RCA apparatus 252.

At step S23, a given sparse measurement (sparse monitoring data) and theselected high resolution component vectors are used to performsuper-resolution reconstruction to generate a dense version of thesparse monitoring data. This is delivered at step S16 for use in processmonitoring and/or control. In summary, when a sparse measurement isachieved on a wafer and sparse monitoring data representing this waferare super-resolution reconstruction can be performed to reconstruct ahigh resolution version of the sparse data based on stored, availablerelevant data (component vectors) representing, for example, densemeasurements such as measurements obtained for each product and layer.

The super-resolution reconstruction step S23, can be implemented forexample by the following steps, starting from a multidimensional vectorM representing a given sparse measurement of CD or other monitoringdata:

(a) Subsample the selected component vectors (PC_(n)) to mimic thesparse sampling scheme of the received monitoring data M. (PC_(n))_(L)can represent the sparse version of the component vector PCn.(b) Determine a best fit based on a least squares criterion, in order tofind a linear combination of the component vectors that best describedthe sparse monitoring data. In mathematical terms, the task is to find aweight factor c_(n) by projecting the measured vector onto thecorresponding component vector (PC_(n))_(L).(c) Sum the original (high density) component vectors (PC_(n)) with theidentified weight factors c_(n) found in step (b) to reconstruct a highresolution version M_(H) of the monitoring data M.

The reconstruction technique applied here is similar to a PCA basedimage reconstruction technique known to be applied in fields related tocomputer vision. The known technique is disclosed in ‘PCA basedGeneralized Interpolation for Image Super-Resolution’ by C. V. Jiji etal., ICVGIP 2004, Proceedings of the Fourth Indian Conference onComputer Vision, Graphics & Image Processing, Kolkata, India, (2004).Note however that the Jiji reference works entirely with low resolutionimages. There is no high resolution object data and no library of highresolution component vectors. There is only a library of low resolution“eigen-images”, which have been obtained by PCA analysis of a databaseof historical face images. Other up-sampling (i.e. resolutionenhancement) techniques, mainly applied for image acquisition andtransmission, are, for example, disclosed in U.S. Pat. No. 6,184,935,US20110081094, U.S. Pat. Nos. 6,603,804, 7,019,777, US20070031065. Amethod and apparatus for the enhancement of images stored in a databaseare disclosed, for example, in U.S. Pat. No. 7,123,780. Face recognitionand reconstruction methods are disclosed, for example, in U.S. Pat. No.7,379,611, US20110305404. The inventors have recognized that teachingfrom any of these references may be applicable to assist implementationof the reconstruction technique for enhanced metrology, as disclosedhere.

It will be understood that the terms “sparse” and “dense” are relativeterms, and no absolute level of spatial resolution is implied by eitherterm. Moreover, what is a high spatial resolution in one context may bea low spatial resolution for another purpose or for another type ofdata.

While the reconstruction method has been described here with animplementation of PCA corresponding to the examples described above withreference to FIGS. 7 to 9, the reconstruction method can also be adaptedto use the alternative implementations described above.

Application Example of Reconstruction to Improve Performance Monitoring

FIG. 21 is a diagram of a workflow representing a performance monitoringfunction comprising a super-resolution method of the type illustratedabove. The performance monitoring function may be implemented in acontroller for, for example, real time process corrections and/or datapre/post-processing in a manufacturing facility such as that shown inFIG. 2. This may be an implementation for example of monitoring step S5of FIG. 12 and may feed into correction step S11 or a separatecorrection step.

At step S30, measurements forming monitoring data become available. Thespatial resolution of the monitoring data is monitored at step S31. Ifthe data is obtained by dense measurements, then at step S32 it may beadded as object data to the library stored at 268 (S6 in FIG. 12). ThePCA analysis may be updated, either immediately or on an occasionalbasis. At step S33, high resolution fingerprints of the monitored waferor lot are estimated in the same manner as the normal performancemonitoring process. For example, spatial and/or temporal smoothing maybe applied to reduce noise in the measurements. At S34, correspondingcorrections are delivered and made available to the controller toimprove performance of subsequent production (S12 of FIG. 2corresponds).

If the new monitoring data is obtained only by sparse measurements,sparse fingerprints are estimated at step S35. Again, this may involvespatial and/or temporal smoothing to reduce the influence of randomnoise in the measurements. At step S36, process indicator PI is testedagainst control limits as described in FIG. 18. If the performanceindicator is outside the control limit CL, flow proceeds to anout-of-control action step S37. Depending on design and on the severityof the errors, the production process may be is stopped, or at least analarm may be sent to the controller. If the performance indicator iswithin limits, then at step S38 it is checked whether relevant PCAresults are available in the library at 268. If suitable results areavailable, then at step S39 a super-resolution reconstruction applied tothe sparse monitoring data. This is performed as described above withreference to FIG. 18. After reconstruction, a high-resolution (dense)version of the monitoring data can be delivered to step S33 for use inperformance monitoring and correction. Before passing to step S33,however, the reconstruction is quality-checked at step S40. If the datareconstruction process of step S39 is judged unsuccessful for somereason, the control again passes to step S37 to trigger anout-of-control action. Back at step S38, in case of insufficient PCAresults available in the library, the performance monitoring functionmay optionally at S41 generate low resolution corrections that can bedelivered to the controller.

Assuming libraries of sufficient size and quality are accessible to theperformance monitoring function, the reconstruction method justdescribed can bridge a gap between sparse and dense measurements in ahigh-volume manufacturing process. With regard to the quality check atS40, it may be for example that the least squares fitting of componentvectors yields only a poor correlation with the received monitoringdata. This indicates that some effect is present in the monitoredwafers, that has not been seen in the historic object data used in thePCA analysis represented in the library. In this way, monitoring processmay be able to send out alarms when current measurements becomesignificantly dissimilar from past observations, for instance, if thevariance of component vectors fit residuals surpasses a specificthreshold for a given application. Note that this quality check can givean early indication of trouble, even though the performance indicatoritself is still well within the control limits.

In conclusion, outputs of the super-resolution reconstruction method mayyield several benefits:

-   -   The SR reconstruction method provides reliable high resolution        corrections that can be applied to each lot, thus improving        yield for critical layers.    -   Metrology effort can be reduced for sub-critical layers with        little performance loss, thus permitting more extensive higher        resolution measurements for critical processes.    -   Performance variation can be detected at an early stage, thus        saving on rework expenditure and allowing for better planning of        dense measurements.

Alternative and/or additional application examples of thesuper-resolution reconstruction (SR) method are, for example, thedetection of subtle process drift (e.g. fingerprint variation overtime). The fingerprint variation is currently monitored by performanceindicators that monitor the variation magnitude, but not the variationspatial profile. Therefore, small process drifts may be undetected untilreaching a ‘critical point’ that may affect the manufacturing process.SR method may be implemented to detect small time variation offingerprints spatial profile.

Alternatively, the SR method, in parallel with sparse measurement, maybe employed for the monitoring of ‘relatively stable’ sub-criticallayers to reduce the frequency of performing high-resolutionmeasurements. In this case, gradual changes of high spatial frequencymay be undetected.

The SR method may also help to improve yield. For example, in case ofcritical layers presenting a high spatial frequency fingerprint thatvaries over time, it is preferable to measure each lot densely; however,as already mentioned, extensive measurements are not feasible inpractice. Using super-resolution reconstruction of dense measurementsfrom sparse measurements allows updates to the processing sub-recipe tobe implemented with a reduced time lag, because it is not necessary towait until the next high-resolution measurement is made.

The SR method can be applied to measurements other than performanceparameters such as CD and overlay. Leveling and/or alignment procedureswithin the lithographic patterning step may also benefit from theimplementation of the SR method within their computational apparatusesand associated processes. For example, during leveling and/or alignmentprocedures, SR method may help in enhancing the spatial resolutionand/or increasing the accuracy of height map and/or level measurementsbased on ‘history’ data. Reducing the density of actual measurements canhelp increase throughput.

The SR method may also help in reducing the amount of scanning electronmicroscope (SEM) measurements needed for the calibration of full chipnumerical simulations to SEM measurements. For example, SEM measurementsmay be carried out for a few layers. The SR method can then be appliedto sparse measurements, to limit metrology expenditure for subsequentjobs.

Hardware Implementation

The steps of the methods described above can be automated within anygeneral purpose data processing hardware (computer), so long as it hasaccess to the object data and, if desired performance data and contextdata. The apparatus may be integrated with existing processors such asthe lithography apparatus control unit LACU shown in FIG. 1 or anoverall process control system. The hardware can be remote from theprocessing apparatus, even being located in a different country.Components of a suitable data processing apparatus (DPA) are shown inFIG. 22. The apparatus may be arranged for loading a computer programproduct comprising computer executable code. This may enable thecomputer assembly, when the computer program product is downloaded, toimplement the functions of the PCA apparatus and/or RCA apparatus asdescribed above.

Memory 1229 connected to processor 1227 may comprise a number of memorycomponents like a hard disk 1261, Read Only Memory (ROM) 1262,Electrically Erasable Programmable Read Only Memory (EEPROM) 1263 orRandom Access Memory (RAM) 1264.

Not all aforementioned memory components need to be present.Furthermore, it is not essential that aforementioned memory componentsare physically in close proximity to the processor 1227 or to eachother. They may be located at a distance away

The processor 1227 may also be connected to some kind of user interface,for instance a keyboard 1265 or a mouse 1266. A touch screen, trackball, speech converter or other interfaces that are known to personsskilled in the art may also be used.

The processor 1227 may be connected to a reading unit 1267, which isarranged to read data, e.g. in the form of computer executable code,from and under some circumstances store data on a data carrier, like afloppy disc 1268 or a CDROM 1269. Also DVD's or other data carriersknown to persons skilled in the art may be used.

The processor 1227 may also be connected to a printer 1270 to print outoutput data on paper as well as to a display 1271, for instance amonitor or LCD (Liquid Crystal Display), of any other type of displayknown to a person skilled in the art.

The processor 1227 may be connected to a communications network 1272,for instance a public switched telephone network (PSTN), a local areanetwork (LAN), a wide area network (WAN) etc. by means oftransmitters/receivers 1273 responsible for input/output (I/O). Theprocessor 1227 may be arranged to communicate with other communicationsystems via the communications network 1272. In an embodiment of theinvention, external computers (not shown), for instance personalcomputers of operators, can log into the processor 1227 via thecommunications network 1272.

The processor 1227 may be implemented as an independent system or as anumber of processing units that operate in parallel, wherein eachprocessing unit is arranged to execute sub-tasks of a larger program.The processing units may also be divided in one or more main processingunits with several sub-processing units. Some processing units of theprocessor 1227 may even be located a distance away of the otherprocessing units and communicate via communications network 1272.Connections between modules can be made wired or wireless.

The computer system can be any signal processing system with analogueand/or digital and/or software technology arranged to perform thefunctions discussed here.

In an embodiment, there is provided a diagnostic apparatus for use inrelation to an industrial process, the apparatus comprising a dataprocessing apparatus programmed to perform the steps of: receivingobject data for a set of product units that have been subjectednominally to the same industrial process, the object data for eachproduct unit representing one or more parameters measured on the productunit at points spatially distributed across the product unit; defining amultidimensional space in which the object data for each of the productunits can be represented as a vector; performing a multivariate analysison the object data to obtain one or more component vectors in themultidimensional space; and extracting diagnostic information about theindustrial process using the component vectors.

In an embodiment, the apparatus is adapted for use where the industrialprocess comprises a sequence of one or more lithographic processingsteps performed on product units in the form of substrates, and arrangedsuch that measurements made automatically in the performance of alithographic patterning operation are captured and represented in theobject data. In an embodiment, the measurements include positionaldeviations measured automatically at locations spatially distributedacross each substrate in performance of the lithographic patterningoperation. In an embodiment, in the vectors the positional deviationsare expressed relative to a corrected position defined by an alignmentmodel calculated from the positional deviations. In an embodiment, theapparatus is arranged to receive for use as the object data spatiallydistributed measurements of one or more of overlay, critical dimension,side wall angle, wafer quality, focus. In an embodiment, the apparatusis arranged to extract diagnostic information at least partly bydesignating certain product units as product units of interest based onthe positions of their vectors when projected onto one or more of thecomponent vectors. In an embodiment, the apparatus is arranged todesignate as being of interest those product units whose vectors occupyoutlying positions when projected onto a selected one of the componentvectors. In an embodiment, the apparatus is arranged to designate asbeing of interest those product units whose vectors occupy an outlyingregion in a plane defined by a selected two or more of the componentvectors. In an embodiment, the apparatus is further arranged to receiveperformance data representing one or more performance parametersmeasured for each product unit and further arranged to designate one ormore of the component axes as being of interest, based on correlationobserved between product units being designated as of interest accordingto the projection of their vectors onto the selected axis(axes) andproduct units designated as of interest according to the performancedata. In an embodiment, the apparatus is adapted for use where theindustrial process comprises a sequence of one or more lithographicprocessing steps performed on product units in the form of substrates,wherein the performance parameters include one or more of overlay,critical dimension, side wall angle, wafer quality, focus. In anembodiment, the apparatus is further arranged to receive context datarepresenting one or more parameters of the industrial process as appliedto each individual product unit, and further programmed to extractdiagnostic information using the context data. In an embodiment, theapparatus is programmed to extract the diagnostic information at leastpartly by identifying correlation between the identification of productunits as being of interest based on the component vectors and one ormore parameters in the context data. In an embodiment, the apparatus isprogrammed to extract diagnostic information by displaying one- ormore-dimensional plots of product unit distribution with selectedparameters from the context data, the product units being represented inthe plots in such a way that product units designated as being ofinterest can be distinguished visually from other product units. In anembodiment, the apparatus is adapted for use where the industrialprocess includes performing one or more lithographic, physical and/orchemical operations by different individual processing apparatuses ondifferent individual product units, and wherein the context dataincludes at least one parameter identifying the individual processingapparatus used for a given operation. In an embodiment, the apparatus isprogrammed to extract diagnostic information at least partly bycomparing vectors representing a particular product unit at differentstages in the industrial process. In an embodiment, the extractingdiagnostic information comprises: receiving sparse object data for oneor more further product units that have been subjected nominally to thesame industrial process as the set of product units, the sparse objectdata for the further product unit(s) representing the one or moreparameters measured on the product unit(s) at points spatiallydistributed across the product unit with a lower density than themeasurements received for the set of product units, analyzing the sparseobject data by reference to at least a subset of the component vectorsidentified by the multivariate analysis; and combining the sparse objectdata with the component vectors in accordance with the result of theanalyzing step, thereby to reconstruct object data representing the oneor more parameters measured on the further product unit(s) at pointsspatially distributed across the product unit with a higher density thanthe sparse object data. In an embodiment, the analyzing the sparseobject data is performed by reference to sparse versions of thecomponent vectors, each sparse version of a component vector beinggenerated by sub-sampling the component vector in accordance with thespatial distribution of the sparse object data. In an embodiment, theapparatus is further programmed to generate correction data for use incontrolling the industrial process. In an embodiment, the apparatus isfurther programmed to generate context criteria for use in determiningto which product units the correction should be applied by comparing thecontext criteria to further context data describing parameters ofindustrial process as applied to the further product units. In anembodiment, the apparatus is adapted for use where the industrialprocess comprises a mixture of lithographic patterning operations andphysical and/or chemical operations, and programmed to generate thecorrection data for applying corrections in a lithographic patterningoperation. In an embodiment, the apparatus further comprises acontroller arranged to control a lithographic apparatus by applyingcorrections based on the extracted diagnostic information. In anembodiment, the object data prior to the multivariate analysis and thecomponent vectors obtained by the multivariate analysis are bothexpressed as vectors in the same multidimensional space.

In an embodiment, there is provided a method of obtaining diagnosticinformation relating to an industrial process, the method comprising:receiving object data for a set of product units that have beensubjected nominally to the same industrial process, the object data foreach product unit representing one or more parameters measured on theproduct unit at points spatially distributed across the product unit;defining a multidimensional space in which the object data for each ofthe product units can be represented as a vector; performing amultivariate analysis on the object data to obtain one or more componentvectors in the multidimensional space; and extracting diagnosticinformation about the industrial process using the component vectors.

In an embodiment, the industrial process comprises a sequence of one ormore lithographic processing steps performed on product units in theform of substrates, each lithographic processing step comprising one ormore lithographic patterning operations followed by one or more physicaland/or chemical processing operations. In an embodiment, measurementsmade automatically in the performance of a lithographic patterningoperation are captured and represented in the object data. In anembodiment, the measurements include positional deviations measuredautomatically using alignment marks spatially distributed across eachsubstrate in performance of the lithographic patterning operation. In anembodiment, in the vectors the positional deviations are expressedrelative to a corrected position defined by an alignment modelcalculated from the positional deviations. In an embodiment, thelithographic processing operation uses an alignment model thatimplements both lower order and higher order corrections, and wherein inthe vectors the positional deviations are expressed relative to acorrected position defined by lower order corrections only. In anembodiment, the method further comprises generating one or more sets ofcorrection data for use in controlling the industrial process whenperformed on further product units. In an embodiment, the extractingdiagnostic information comprises: receiving sparse object data for oneor more further product units that have been subjected nominally to thesame industrial process as the set of product units, the sparse objectdata for the further product unit(s) representing the one or moreparameters measured on the product unit(s) at points spatiallydistributed across the product unit with a lower density than themeasurements received for the set of product units, analyzing the sparseobject data by reference to at least a subset of the component vectorsidentified by the multivariate analysis, and combining the sparse objectdata with the component vectors in accordance with the result of theanalyzing step, thereby to reconstruct object data representing the oneor more parameters measured on the further product unit(s) at pointsspatially distributed across the product unit with a higher density thanthe sparse object data. In an embodiment, the analyzing the sparseobject data is performed by reference to sparse versions of thecomponent vectors, the sparse versions of the component vectors beinggenerated by sub-sampling the component vectors in accordance with thespatial distribution of the sparse object data. In an embodiment, theobject data prior to the multivariate analysis and the component vectorsobtained by the multivariate analysis are both expressed as vectors inthe same multidimensional space.

In an embodiment, there is provided a method of controlling anindustrial process in which product units are subjected to one or moreprocessing operations, the method comprising: measuring a plurality ofproduct units that have been subjected to some or all of the processingoperations to obtain object data representing for each product unit oneor more parameters measured on the product unit at points spatiallydistributed across the product unit; using the object data to obtaindiagnostic information by an apparatus as described herein or a methodas described herein; and controlling the performance of the industrialprocess for subsequent product units based on the extracted diagnosticinformation. In an embodiment, the industrial process is a lithographicprocess for the manufacture of semiconductor devices, the processingoperations including lithographic pattering operations and one or morephysical and/or chemical processing operations, the product unitscomprising substrates, wherein the object data includes alignment datameasured from the substrates in the course of at least one of thelithographic pattering operations. In an embodiment, the industrialprocess is a lithographic process for the manufacture of semiconductordevices, the processing operations including lithographic patteringoperations and one or more physical and/or chemical processingoperations, the product units comprising substrates, wherein the step ofcontrolling the performance of the industrial process includesselectively applying alignment corrections in at least one of thelithographic pattering operations. In an embodiment, the industrialprocess is a lithographic process for the manufacture of semiconductordevices, the processing operations including lithographic patteringoperations and one or more physical and/or chemical processingoperations, the product units comprising substrates, wherein the objectdata includes at least one performance parameter measured from thesubstrates after performance of at least one of the lithographicpattering operations. In an embodiment, the extracting diagnosticinformation comprises: receiving sparse object data for one or morefurther product units that have been subjected nominally to the sameindustrial process as the set of product units, the sparse object datafor the further product unit(s) representing the one or more parametersmeasured on the product unit(s) at points spatially distributed acrossthe product unit with a lower density than the measurements received forthe set of product units, analyzing the sparse object data by referenceto at least a subset of the component vectors identified by themultivariate analysis, and combining the sparse object data with thecomponent vectors in accordance with the result of the analyzing step,thereby to reconstruct object data representing the one or moreparameters measured on the further product unit(s) at points spatiallydistributed across the product unit with a higher density than thesparse object data. In an embodiment, the decomposing the sparse objectdata is performed by reference to sparse versions of the componentvectors, each sparse version of a component vector being generated bysub-sampling the component vector in accordance with the spatialdistribution of the sparse object data.

In an embodiment, there is provided a computer program productcomprising machine readable instructions for causing a general purposedata processing apparatus to implement a diagnostic apparatus asdescribed herein or to perform a method as described herein.

In an embodiment, the computer program product further comprises machinereadable instructions for causing the data processing apparatus togenerate correction data and correction criteria by implementing adiagnostic apparatus as described herein or by performing a method asdescribed herein.

In an embodiment, there is provided a method of controlling alithographic apparatus wherein corrections are applied based ondiagnostic information extracted from object data by an apparatus asdescribed herein or a method as described herein.

Although specific reference may be made in this text to the use oflithographic apparatus in the manufacture of ICs, it should beunderstood that the lithographic apparatus described herein may haveother applications, such as the manufacture of integrated opticalsystems, guidance and detection patterns for magnetic domain memories,flat-panel displays, liquid-crystal displays (LCDs), thin-film magneticheads, etc. As already mentioned, embodiments of the invention may beapplied in industrial processing applications quite separate fromlithography. Examples might be in production of optical components,automotive manufacture, construction—any number of applications whereobject data exists in the form of measurements made with a certainspatial distribution over the product. As in the example of lithography.the set of measurements that is subjected to multivariate analysis canbe measurements made for different product units, and/or differentinstances of measuring the same product units. Although specificreference may have been made above to the use of embodiments of theinvention in the context of optical lithography, it will be appreciatedthat an embodiment of the invention may be used in other types oflithography, for example imprint lithography, and where the contextallows, is not limited to optical lithography. In imprint lithography atopography in a patterning device defines the pattern created on asubstrate. The topography of the patterning device may be pressed into alayer of resist supplied to the substrate whereupon the resist is curedby applying electromagnetic radiation, heat, pressure or a combinationthereof. The patterning device is moved out of the resist leaving apattern in it after the resist is cured.

The terms “radiation” and “beam” used herein encompass all types ofelectromagnetic radiation, including ultraviolet (UV) radiation (e.g.having a wavelength of or about 365, 248, 193, 157 or 126 nm) andextreme ultra-violet (EUV) radiation (e.g. having a wavelength in therange of 5-20 nm), as well as particle beams, such as ion beams orelectron beams.

The descriptions above are intended to be illustrative, not limiting.Thus, it will be apparent to one skilled in the art that modificationsmay be made to the invention as described without departing from thespirit and scope of the claims set out below. In addition, it should beappreciated that structural features or method steps shown or describedin any one embodiment herein can be used in other embodiments as well.

1-42. (canceled)
 43. A method comprising: obtaining object data for aset of physical product units that have been subjected nominally to asame device manufacturing process; obtaining context data representingall or part of the processing history of each product unit of the set ofproduct units; decomposing, by a hardware computer system, the objectdata into one or more fingerprint components; and diagnosing, by thehardware computer system, the device manufacturing process based on thecontext data and the one or more obtained fingerprint components. 44.The method of claim 43, wherein the diagnosing comprises correlating theone or more fingerprint components to one or more parameters comprisedwithin the context data.
 45. The method of claim 43, wherein the contextdata identifies a particular apparatus, or part of an apparatus,involved in processing of a product unit from the set of product units.46. The method of claim 43, wherein the diagnosing is a root causeanalysis process.
 47. The method of claim 46, wherein the root causeanalysis process is arranged to extract diagnostic information at leastpartly by designating each of one or more certain product units from theset of product units as a product unit of interest based on the positionof the fingerprint of the respective product unit of the one or morecertain product units when projected onto one or more fingerprintcomponents selected from the one or more fingerprint components.
 48. Themethod of claim 47, further comprising controlling a lithographicapparatus using a correction based on the extracted diagnosticinformation.
 49. The method of claim 48, wherein the correction isconfigured to correct a fingerprint arising from one or more physicaland/or chemical operations to which physical product units have beensubjected.
 50. The method of claim 43, wherein the object data for eachproduct unit comprises a residual resulting from one or more parametersmeasured on the product unit at points spatially distributed across theproduct unit being subjected to a correction obtainable in the devicemanufacturing process.
 51. The method of claim 43, wherein the contextdata represents one or more selected from: a type of process stepapplied to a physical product unit, which one or more individualapparatuses have been used in the performance of a process step appliedto a physical product unit, and/or what one or more parameters wereapplied by one or more individual apparatuses used in the performance ofa process step applied to a physical product unit.
 52. The method ofclaim 43, wherein the decomposing is based on a multivariate analysis.53. The method of claim 43, wherein the object data comprises one ormore selected from: height map data, alignment data, and/or overlay dataand the diagnosing comprises determining a correction based on thecontext data and the one or more fingerprint components, and based onthe determined correction, outputting electronic data for configurationor modification of the device manufacturing process or of a measurementprocess of physical product units subjected to the device manufacturingprocess.
 54. A method comprising: obtaining object data for a set ofphysical product units that have been subjected nominally to a samedevice manufacturing process; obtaining context data representing all orpart of the processing history of each product unit of the set ofproduct units; decomposing the object data into one or more fingerprintcomponents; correlating, by a hardware computer system, the context datato the one or more fingerprint components; determining, by the hardwarecomputer system, a correction based on the correlation between thecontext data and the one or more fingerprint components; and based onthe determined correction, outputting electronic data for configurationor modification of the device manufacturing process or of a measurementprocess of physical product units subjected to the device manufacturingprocess.
 55. The method of claim 54, wherein the correction is specificfor an individual product unit from the set of product units.
 56. Themethod of claim 54, wherein the correction is specific for a batch orlot of product units from the set of product units.
 57. The method ofclaim 54, wherein the correction comprises configuration or modificationof an alignment system of a lithographic apparatus.
 58. The method ofclaim 57, wherein the correction comprises an alignment recipe for alithographic apparatus.
 59. A method comprising: obtaining object datacomprising height map data and/or alignment data, for a set of physicalproduct units that have been subjected nominally to a same devicemanufacturing process; obtaining overlay data measured for each productunit of the set of product units; decomposing the object data into oneor more fingerprint components; correlating, by a hardware computersystem, the overlay data to the one or more fingerprint components;determining, by the hardware computer system, a correction based on thecorrelation between the overlay data and the one or more fingerprintcomponents; and based on the determined correction, outputtingelectronic data for configuration or modification of the devicemanufacturing process or of a measurement process of physical productunits subjected to the device manufacturing process.
 60. The method ofclaim 59, wherein the object data for each product unit comprises aresidual resulting from a height map and/or alignment map measured onthe product unit at points spatially distributed across the product unitbeing subjected to a correction obtainable in the device manufacturingprocess.
 61. The method of claim 59, wherein the correction is specificfor an individual physical product unit out of the set of physicalproduct units.
 62. The method of claim 59, wherein the correction isspecific for a batch or lot of physical product units out of the set ofphysical product units.
 63. A non-transitory computer program productcomprising machine readable instructions, that when executed by acomputer system, are configured to cause the computer system to at leastperform the method of claim
 59. 64. A non-transitory computer programproduct comprising machine readable instructions, that when executed bya computer system, are configured to cause the computer system to atleast perform the method of claim
 43. 65. A non-transitory computerprogram product comprising machine readable instructions, that whenexecuted by a computer system, are configured to cause the computersystem to at least perform the method of claim 54.